Updated on 2024/07/28

Information

 

写真a

 
GAINA MIRCEA DANIEL
 
Organization
Institute of Mathematics for Industry Associate Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Associate Professor
Contact information
メールアドレス
Tel
0928024425
Profile
My research is focused on algebraic specification, one of the most promising aproach to formal methods assisting the developing of software systems at several stages such as design, specification and formal verification. Algebraic specification and programming languages are rigorously based on logic, which amounts to the existence of a logical system underlying the language such that each language feature and construction can be expressed as a mathematical entity of the underlying logic.

Degree

  • BSc in informatics from University of Bucharest

  • Master's degree in fundamentals of informatics from University of Bucharest

  • Master's degree in algebraic specification from Normal Superior School of Bucharest

  • PhD in information science from Japan Advanced Institute of Science and Technology

Research History

  • October 2004 - October 2006: research assistant at University of Bucharest October 2009 - July 2010: postdoctoral researcher at Japan Advanced Institute of Science and Technology August 2010 - March 2013: research assistant professor at Japan Advanced Institute of Science and Technology April 2013 - March 2017: assistant professor at Japan Advanced Institute of Science and Technology April 2017 - March 2022: assistant professor at Kyushu University April 2022 - present: associate professor at Kyushu University   

Research Interests・Research Keywords

  • Research theme: Reconfigurable systems are found everywhere: software-driven medical devices (such as infusion pumps, pacemakers, imaging machines and pill cameras), intelligent transportation systems, cars, or mobile robots. They all interact with their users and the environment in which they operate. Reconfigurable systems are often used in safety-critical areas where any malfunction may cause serious injuries to human beings. The safety requirements can be fulfilled only by applying formal methods. The objective is to develop a software tool for the formal specification and verification of reconfigurable systems.

    Keyword: theorem proving, reconfiguration paradigm, hybrid systems, verification methodology

    Research period: 2023.4 - 2026.4

  • Research theme: Recent developments of computer systems have triggered a paradigm shift from standard applications with fixed resources to reconfigurable systems, i.e. applications that work in different operation modes, called configurations, and react flexibly to internal and external stimuli for optimizing their performance. Very often the operation of reconfigurable systems is safety-critical: any malfunction may result in the serious injury to people. The safety requirements can be fulfilled only by applying formal methods. The purpose is to provide a solid logic-based foundation for developing a formal method to describe reconfigurable systems and to reason formally about their properties.

    Keyword: reconfigurable systems, formal methods, hybrid-dynamic logics

    Research period: 2020.4 - 2023.4

Papers

  • Forcing and Calculi for Hybrid Logics Reviewed International journal

    Daniel Găină

    Journal of the Association for Computing Machinery   67 ( 4 )   1 - 55   2020.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics expressive enough to allow references to the nodes/states/worlds of the models regarded as relational structures, or multi-graphs. Applications of hybrid logics involve many areas of research such as computational linguistics, transition systems, knowledge representation, artificial intelligence, biomedi- cal informatics, semantic networks and ontologies. The present contribution sets a unified foundation for developing formal verification methodologies to reason about Kripke structures by defining proof calculi for a multitude of hybrid logics in the framework of stratified institutions. In order to prove completeness, the paper introduces a forcing technique for stratified institutions with nominal and frame extraction and studies a forcing property based on syntactic consistency. The proof calculus is shown to be complete and the significance of the general results is exhibited on a couple of benchmark examples of hybrid logical systems.

    DOI: https://doi.org/10.1145/3400294

    Other Link: https://dl.acm.org/doi/10.1145/3400294

    Repository Public URL: https://hdl.handle.net/2324/7172111

  • Forcing, Transition Algebras, and Calculi Reviewed International journal

    #Go Hashimoto, Daniel Găină, Ionuţ Ţuţu

    51st EATCS International Colloquium on Automata, Languages and Programming, ICALP 2024   2024.5

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition relations, which are treated similarly to the actions used in dynamic logics in order to define necessity and possibility operators. This leads to a higher degree of expressivity than that of many-sorted first-order logic. For example, one can finitely axiomatize both the finiteness and the reachability of models, neither of which are ordinarily possible in many-sorted first-order logic. We introduce syntactic entailment and study basic properties such as compactness and completeness, showing that the latter does not hold when standard finitary proof rules are used. Consequently, we define proof rules having both finite and countably infinite premises, and we provide conditions under which completeness can be proved. To that end, we generalize the forcing method introduced in model theory by Robinson from a single signature to a category of signatures, and we apply it to obtain a completeness result for signatures that are at most countable.

  • Omitting Types Theorem in hybrid dynamic first-order logic with rigid symbols Reviewed International journal

    Daniel Găină, Guillermo Badia, Tomasz Kowalski

    Annals of Pure and Applied Logic   174 ( 3 )   2023.3

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    In the the present contribution, we prove an Omitting Types Theorem (OTT) for an arbitrary fragment of hybrid dynamic first-order logic with rigid symbols (i.e. symbols with fixed interpretations across worlds) closed under negation and retrieve. The logical framework can be regarded as a parameter and it is instantiated by some well-known hybrid and/or dynamic logics from the literature. We develop a forcing technique and then we study a forcing property based on local satisfiability, which lead to a refined proof of the OTT. For uncountable signatures, the result requires compactness, while for countable signatures, compactness is not necessary. We apply the OTT to obtain upwards and downwards Lowenheim-Skolem theorems for our logic, as well as a completeness theorem for its constructor-based variant.

    DOI: https://doi.org/10.1016/j.apal.2022.103212

  • Robinson consistency in many-sorted hybrid first-order logics Reviewed International journal

    Daniel Găină, Guillermo Badia, Tomasz Kowalski

    Advances in Modal Logic 2022, AiML 2022, Rennes, August 22-25   2022.8

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    In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem.

  • Lindström’s theorem, both syntax and semantics free Reviewed International journal

    Daniel Găină, Tomasz Kowalski

    Journal of Logic and Computation   32 ( 5 )   942 - 975   2022.7

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    Lindström’s theorem characterizes first-order logic in terms of its essential model theoretic properties. One cannot gain expressive power extending first-order logic without losing at least one of compactness or downward Löwenheim–Skolem property. We cast this result in an abstract framework of institution theory, which does not assume any internal structure either for sentences or for models, so it is more general than the notion of abstract logic usually used in proofs of Lindström’s theorem; indeed, it can be said that institutional model theory is both syntax and semantics free. Our approach takes advantage of the methods of institutional model theory to provide a structured proof of Lindström’s theorem at a level of abstraction applicable to any logical system that is strong enough to describe its own concept of isomorphism and its own concept of elementary equivalence. We apply our results to some logical systems formalized as institutions and widely used in computer science practice.

    DOI: https://doi.org/10.1093/logcom/exab073

  • Fraïssé-Hintikka Theorem in institutions Reviewed International journal

    Daniel Găină, Tomasz Kowalski

    Journal of Logic and Computation   30 ( 7 )   1377 - 1399   2020.10

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    We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbitrary institutions whose sentences are finitary. These include many-sorted first-order logic, higher-order logic with types, as well as a number of other logics arising in connection to specification languages. The gain for the classical case is that the characterization is proved directly for all signatures, including infinite ones.

    DOI: https://doi.org/10.1093/logcom/exaa042

    Other Link: https://academic.oup.com/logcom/article-abstract/30/7/1377/5900766

  • Stability of termination and sufficient-completeness under pushouts via amalgamation Reviewed International journal

    Daniel Găină, Masaki Nakamura, Kazuhiro Ogata, Kokichi Futatsugi

    Theoretical Computer Science   848   82 - 105   2020.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    In the present study, we provide conditions for the existence of pushouts of signature morphisms in constructor-based order-sorted algebra, and then we prove that reducibility and termination of term rewriting systems are closed under pushouts. Under the termination assumption, reducibility is equivalent to sufficient-completeness, which is crucial for proving several important properties in computing for constructor-based logics such as completeness, existence of initial models and interpolation. In logic frameworks that are not based on constructors, sufficient-completeness is essential to establish the soundness of the induction schemes which are based on some methodological constructor operators. We discuss the application of our results to the instantiation of parameterized specifications.

    DOI: https://doi.org/10.1016/j.tcs.2020.09.024

    Other Link: https://www.sciencedirect.com/science/article/pii/S0304397520305235?via%3Dihub

  • Birkhoff Completeness for Hybrid-Dynamic First-Order Logic

    Daniel Găină, Ţuţu Ionuţ

    28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019 Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings   277 - 293   2019.8

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    Language:English   Publishing type:Research paper (other academic)  

    Hybrid-dynamic first-order logic is a kind of modal logic obtained by enriching many-sorted first-order logic with features that are common to hybrid and to dynamic logics. This provides us with a logical system with an increased expressive power thanks to a number of distinctive attributes: first, the possible worlds of Kripke structures, as well as the nominals used to identify them, are endowed with an algebraic structure; second, we distinguish between rigid symbols, which have the same interpretation across possible worlds – and thus provide support for the standard rigid quantification in modal logic – and flexible symbols, whose interpretation may vary; third, we use modal operators over dynamic-logic actions, which are defined as regular expressions over binary nominal relations. In this context, we propose a general notion of hybrid-dynamic Horn clause and develop a proof calculus for the Horn-clause fragment of hybrid-dynamic first-order logic. We investigate soundness and compactness properties for the syntactic entailment system that corresponds to this proof calculus, and prove a Birkhoff-completeness result for hybrid-dynamic first-order logic.

    DOI: 10.1007/978-3-030-29026-9_16

  • Specification and Verification of Invariant Properties of Transition Systems

    Daniel Gaina, Ionut Tutu, Adrian Riesco

    25th Asia-Pacific Software Engineering Conference, APSEC 2018 Proceedings - 25th Asia-Pacific Software Engineering Conference, APSEC 2018   99 - 108   2018.7

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    Language:English   Publishing type:Research paper (other academic)  

    Transition systems provide a natural way to specify and reason about the behaviour of discrete systems, and in particular about the computations that they may perform. This paper advances a verification method for transition systems whose reachable states are described explicitly by membership axioms. The proof technique is implemented in the Constructor-based Inductive Theorem Prover (CITP), a proof management tool built on top of a variation of conditional equational logic enhanced with many modern features. This approach complements the so-called OTS method, a verification procedure for observational transition systems that is already implemented in CITP.

    DOI: 10.1109/APSEC.2018.00024

  • Birkhoff style calculi for hybrid logics Reviewed International journal

    Daniel Găină

    Formal Aspects of Computing   29 ( 5 )   805 - 832   2017.9

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    We develop an abstract proof calculus for hybrid logics whose sentences are (hybrid) Horn clauses, and we prove a Birkhoff completeness theorem for hybrid logics in the general setting provided by the institution theory. This result is then applied to particular cases of hybrid logics with user-defined sharing, where the first-order variables in quantified sentences are interpreted uniformly across worlds.

    DOI: 10.1007/s00165-016-0414-y

  • Downward Löwenheim-Skolem Theorem and interpolation in logics with constructors Invited Reviewed International journal

    Daniel Găină

    Journal of Logic and Computation   27 ( 6 )   1717 - 1752   2017.9

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    The present article describes a method for proving Downward Löwenheim-Skolem Theorem within an arbitrary institution satisfying certain logic properties. In order to demonstrate the applicability of the present approach, the abstract results are instantiated to many-sorted first-order logic and preorder algebra. In addition to the first technique for proving Downward Löwenheim-Skolem Theorem, another one is developed, in the spirit of institution-independent model theory, which consists of borrowing the result from a simpler institution across an institution comorphism. As a result, the Downward Löwenheim- Skolem Property is exported from first-order logic to partial algebras, and from higher-order logic with intensional Henkin semantics to higher-order logic with extensional Henkin semantics. The second method successfully extends the domain of application of Downward Löwenheim-Skolem Theorem to other non-conventional logical systems for which the first technique may fail. One major application of Downward Löwenheim-Skolem Theorem is interpolation in constructor-based logics with universally quantified sentences. The interpolation property is established by borrowing it from a base institution for its constructor-based variant across an institution morphism. This result is important as interpolation for constructor-based first-order logics is still an open problem.

    DOI: 10.1093/logcom/exv018

  • Foundations of logic programming in hybrid logics with user-defined sharing Reviewed International journal

    Daniel Găină

    Theoretical Computer Science   686   1 - 24   2017.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    The present contribution advances an abstract notion of hybrid logic by supplementing the definition of institution with an additional structure to extract frames. The foundation of logic programming is set in the general framework proposed by defining the basic concepts such as Horn clause, query and solution, and proving fundamental results such as the existence of initial model of Horn clauses and Herbrand's theorem. The abstract results are then applied to hybrid logics with user-defined sharing, where the possible worlds share a common domain and the variables used for quantification are interpreted uniformly across the worlds.

    DOI: 10.1016/j.tcs.2017.04.009

  • Initial semantics in logics with constructors Reviewed International journal

    Daniel Găină, Kokichi Futatsugi

    Journal of Logic and Computation   25 ( 1 )   95 - 116   2015.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    The constructor-based logics constitute the logical foundation of the so-called OTS/CafeOBJ method, a modelling, specification and verification method of the observational transition systems. The important role played in algebraic specifications by the initial algebras semantics is well known. Free models along presentation morphisms provide semantics for the modules with initial denotation in structured specification languages. Following Goguen and Burstall, the notion of logical system over which we build specifications is formalized as an institution. The present work is an institution-independent study of the existence of free models along sufficient complete presentation morphisms in logics with constructors in the signatures.

    DOI: 10.1093/logcom/exs044

  • Foundations of logic programming in hybridised logics

    Daniel Găină

    22nd International Workshop on Recent Trends in Algebraic Development Techniques, WADT 2014 Recent Trends in Algebraic Development Techniques - 22nd International Workshop, WADT 2014, Revised Selected Papers   69 - 89   2015.1

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    Language:English   Publishing type:Research paper (other academic)  

    The present paper sets the foundation of logic programming in hybridised logics. The basic logic programming semantic concepts such as query and solutions, and the fundamental results such as the existence of initial models and Herbrand’s theorem, are developed over a very general hybrid logical system.We employ the hybridisation process proposed by Diaconescu over an arbitrary logical system captured as an institution to define the logic programming framework.

    DOI: 10.1007/978-3-319-28114-8_5

  • Proving sufficient completeness of constructor-based algebraic specifications Reviewed

    Masaki Nakamura, Daniel Gaina, Kazuhiro Ogata, Kokichi Futatsugi

    Lecture Notes in Electrical Engineering   373   15 - 21   2015.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    OBJ algebraic specification languages, for example, OBJ3, CafeOBJ and Maude, are formal specification languages which support several sophisticated functions to describe and verify large and complex specifications. Recently, the proof score method, which is an interactive formal verification method for OBJ languages, based on constructor-based algebras has been developed and several practical case studies have been reported. Sufficient completeness is one of the most important properties of constructor-based specifications, which guarantees the existence of initial models. In this study, we give a sufficient condition for sufficient completeness of constructor-based specifications based on the theory of term rewriting.

    DOI: 10.1007/978-981-10-0281-6_3

  • Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally Reviewed

    Daniel Mircea Gaina

    Logica Universalis   8 ( 3-4 )   469 - 498   2014.12

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    In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove two abstract results: Downward Löwenheim-Skolem Theorem (DLST) and Omitting Types Theorem (OTT). We instantiate these general results to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulas by means of Boolean connectives and classical first-order quantifiers. These include first-order logic (FOL), logic of order-sorted algebras (OSA), preorder algebras (POA), as well as their infinitary variants FOL ω1, ω, OSA ω1, ω, POA ω1, ω. In addition to the first technique for proving OTT, we develop another one, in the spirit of institution-independent model theory, which consists of borrowing the Omitting Types Property (OTP) from a simpler institution across an institution comorphism. As a result we export the OTP from FOL to partial algebras (PA) and higher-order logic with Henkin semantics (HNK), and from the institution of FOLω1, ω to PAω1, ω and HNKω1, ω. The second technique successfully extends the domain of application of OTT to non conventional logical systems for which the standard methods may fail.

    DOI: 10.1007/s11787-013-0090-0

  • On automation of OTS/CafeOBJ method Reviewed

    Daniel Gǎinǎ, Dorel Lucanu, Kazuhiro Ogata, Kokichi Futatsugi

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   8373   578 - 602   2014.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    The proof scores method is an interactive verification method in algebraic specification that combines manual proof planning and reduction (automatic inference by rewriting). The proof score approach to software verification coordinates efficiently human intuition and machine automation. We are interested in applying these ideas to transition systems, more concretely, in developing the so-called OTS/CafeOBJ method, a modelling, specification, and verification method of observational transition systems. In this paper we propose a methodology that aims at developing automatically proof scores according to the rules of an entailment system. The proposed deduction rules include a set of generic rules, which can be found in other proof systems as well, together with a set of rules specific to our working context. The methodology is exhibited on the example of the alternating bit protocol, where the unreliability of channels is faithfully specified.

    DOI: 10.1007/978-3-642-54624-2_29

  • Constructor-based inductive theorem prover

    Daniel Gǎinǎ, Min Zhang, Yuki Chiba, Yasuhito Arimoto

    5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013 Algebra and Coalgebra in Computer Science - 5th International Conference, CALCO 2013, Proceedings   328 - 333   2013.10

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    Language:English   Publishing type:Research paper (other academic)  

    Constructor-based Theorem Prover (CITP) is a tool for proving inductive properties of software systems specified with constructor-based logics. CITP is equipped with a default proof strategy for the automated verification of Observational Transitional Systems (OTS), but the area of applications is not restricted to OTS. The proof strategy can be customised by the user, or the basic tactics can be applied step-by-step. The tool features are exhibited on concrete examples, showing how to perform verification with CITP.

    DOI: 10.1007/978-3-642-40206-7-26

  • Interpolation in logics with constructors Reviewed

    Daniel Gǎinǎ

    Theoretical Computer Science   474   46 - 59   2013.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    We present a generic method for establishing the interpolation property by borrowing it across the logical systems from a base institution to prove it for its constructor-based variant. The framework used is that of the so-called institution theory invented by Goguen and Burstall which is a categorical-based formulation of the informal concept of logical system sufficiently abstract to capture many examples of logics used in computer science and mathematical logic, and expressive enough to elaborate our general results. We illustrate the applicability of the present work by instantiating the abstract results to constructor-based Horn clause logic and constructor-based Horn preorder algebra but applications are also expected for many other logical systems.

    DOI: 10.1016/j.tcs.2012.12.002

  • Principles of proof scores in CafeOBJ Invited Reviewed International journal

    Kokichi Futatsugi, Daniel Găină, Kazuhiro Ogata

    Theoretical Computer Science   464   90 - 112   2012.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    This paper describes the theoretical principles of a verification method with proof scores in the CafeOBJ algebraic specification language. The verification method focuses on specifications with conditional equations and realizes systematic theorem proving (or interactive verification). The method is explained using a simple but instructive example, and the necessary theoretical foundations, which justify every step of the verification, are described with precise mathematical definitions. Some important theorems that result from the definitions are also presented.

    DOI: 10.1016/j.tcs.2012.07.041

  • Constructor-based logics Reviewed

    Daniel Gǎinǎ, Kokichi Futatsugi, Kazuhiro Ogata

    Journal of Universal Computer Science   18 ( 16 )   2204 - 2233   2012.12

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    Many computer science applications concern properties that are true for a restricted class of models. In this paper, a couple of constructor-based institutions are presented. These institutions are defined on top of some base institutions, roughly speaking, by enhancing the syntax with constructor symbols and restricting the semantics to models with elements that are reachable by constructors. The proof rules for the constructor-based Horn logics, formalized as institutions, are defined in this paper, and a proof of completeness is provided in the abstract framework of institutions.

  • Completeness by forcing Reviewed International journal

    Daniel Găină, Marius Petria

    Journal of Logic and Computation   20 ( 6 )   1165 - 1186   2010.12

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    The completeness of the infinitary language ℒ ω1,ω was proved by Carol Karp in 1964.We express and prove the completeness of infinitary first-order logics in the institution-independent setting by using forcing, a powerful method for constructing models. As a consequence of this abstraction, the completeness theorem becomes available for the infinitary versions of many 'first order' logical systems that appear in the area of logic or computer science.

    DOI: 10.1093/logcom/exq012

  • Constructor-based institutions

    Daniel Gǎinǎ, Kokichi Futatsugi, Kazuhiro Ogata

    3rd International Conference on Algebra and Coalgebra in Computer Science, CALCO 2009 Algebra and Coalgebra in Computer Science - Third International Conference, CALCO 2009, Proceedings   398 - 412   2009.11

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    Many computer science applications concern properties which are true of a restricted class of models. We present a couple of constructor-based institutions defined on top of some base institutions by restricting the class of models. We define the proof rules for these logics formalized as institutions, and prove their completeness in the abstract framework of institutions.

    DOI: 10.1007/978-3-642-03741-2_27

  • Birkhoff completeness in institutions Reviewed International journal

    Mihai Codescu, Daniel Găină

    Logica Universalis   2 ( 2 )   277 - 309   2008.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    We develop an abstract proof calculus for logics whose sentences are 'Horn sentences' of the form: (∀X)H ⇒ c and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the 'Horn fragment' of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.

    DOI: 10.1007/s11787-008-0035-1

  • Erratum An institution-independent generalization of tarski's elementary chain theorem (Journal of Logic and Computation (2006) 16 (713-735) DOI: 10.1093/logcom/exl006) Reviewed

    Daniel Gǎinǎ, Andrei Popescu

    Journal of Logic and Computation   17 ( 3 )   2007.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1093/logcom/exm022

  • An institution-independent proof of the Robinson Consistency Theorem Reviewed International journal

    Daniel Găină, Andrei Popescu

    Studia Logica   85 ( 1 )   41 - 73   2007.2

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    We prove an institutional version of A. Robinson's Consistency Theorem. This result is then appliedto the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

    DOI: 10.1007/s11225-007-9022-4

  • An institution-independent generalization of Tarski's elementary chain theorem Reviewed

    Daniel Gǎinǎ, Andrei Popescu

    Journal of Logic and Computation   16 ( 6 )   2006.12

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    We prove an institutional version of Tarski's elementary chain theorem applicable to a whole plethora of 'first-orderaccessible' logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulae by means of classical first-order connectives and quantifiers. These include the unconditional equational, positive, (π ∪ ∑)n 0 and full first-order logics, as well as less conventional logics, used in computer science, such as hidden or rewriting logic.

    DOI: 10.1093/logcom/exl006

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Presentations

  • Forcing and its applications in hybrid logics Invited International conference

    Daniel Găină

    Section of Mathematical Sciences of the Romanian Academy, the Romanian Mathematical Society, the Simion Stoilow Institute of Mathematics of the Romanian Academy, the Faculty of Mathematics and Computer Science of the University of Bucharest  2019.7 

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    Event date: 2020.6 - 2020.7

    Language:English  

    Venue:"Dunărea de Jos" University of Galati   Country:Romania  

    The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics expressive enough to allow references to the nodes/states/worlds of the models regarded as relational structures, or multi-graphs. Applications of hybrid logics involve many areas of research such as computational linguistics, transition systems, knowledge representation, artificial intelligence, biomedi- cal informatics, semantic networks and ontologies. The present contribution sets a unified foundation for developing formal verification methodologies to reason about Kripke structures by defining proof calculi for a multitude of hybrid logics in the framework of stratified institutions. In order to prove completeness, we introduce a forcing technique for stratified institutions with nominal and frame extraction and studies a forcing property based on syntactic consistency. The proof calculus is shown to be complete and the significance of the general results is exhibited on a couple of benchmark examples of hybrid logical systems.

    Other Link: https://sites.google.com/view/congmatro9/home

  • Birkhoff style proof systems for hybrid-dynamic quantum logic Invited International conference

    Daniel Găină

    Formal verification of quantum circuits/protocols/programs, Japan Advanced Institute for Science and Technology  2024.1 

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    Event date: 2024.1

    Language:English   Presentation type:Symposium, workshop panel (public)  

    Country:Japan  

    We explore a simple approach to quantum logic based on hybrid and dynamic modal logic, where the set of states is given by some Hilbert space. In this setting, a notion of quantum clause is proposed in a similar way the notion of Horn clause is advanced in first-order logic, that is, to give logical properties for use in logic programming and formal specification. We propose proof rules for reasoning about quantum clauses and we investigate soundness and compactness properties that correspond to this proof calculus. Then we prove a Birkhoff completeness result for the fragment of hybrid- dynamic quantum logic determined by quantum clauses.

  • Initiality in Hybrid-Dynamic Quantum Logic Invited International conference

    Daniel Găină

    Cracow Logic Conference (CLoCk)  2023.6 

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    Event date: 2023.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Department of Logic, Institute of Philosophy, Jagiellonian University, Kraków   Country:Poland  

  • Robinson consistency in many-sorted hybrid first-order logics International conference

    Daniel Găină

    Advances in Modal Logic, AiML 2022  2022.8 

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    Event date: 2022.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institute for Research in Computer Science and Random Systems, Rennes   Country:France  

  • Stability of termination under pushouts via amalgamation International conference

    Daniel Găină

    Australian and New Zealand Industrial and Applied Mathematics  2022.2 

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    Event date: 2022.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:online   Country:Australia  

    Other Link: https://anziam2022.com.au

  • Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols International conference

    Daniel Găină

    Mathematical Society of Japan  2021.9 

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    Event date: 2021.9

    Language:English   Presentation type:Oral presentation (general)  

    Venue:online   Country:Japan  

    Other Link: https://www.mathsoc.jp/en/meeting/chiba21sept/

  • Stability of termination under pushouts via amalgamation

    Daniel Găină

    32nd Seminar on Algebra, Logic and Geometry in Informatics (ALGI)  2021.9 

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    Event date: 2021.9

    Language:English   Presentation type:Oral presentation (general)  

    Venue:online   Country:Japan  

  • Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols International conference

    Daniel Găină

    The Australasian Association for Logic  2021.6 

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    Event date: 2021.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:online   Country:Australia  

    Other Link: https://blogs.unimelb.edu.au/logic/aal-2021/

  • Forcing and Calculi for Hybrid Logics International conference

    Daniel Găină

    Australasian Logic Group  2020.12 

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    Event date: 2020.12

    Language:English  

    Venue:online   Country:Japan  

  • Specification and Verification of Invariant Properties of Transition Systems International conference

    Daniel Găină

    25th Asia-Pacific Software Engineering Conference (APSEC 2018)  2018.12 

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    Event date: 2020.11

    Language:English  

    Country:Japan  

  • Forcing and Calculi for Hybrid Logics

    Daniel Găină

    31st Seminar on Algebra, Logic and Geometry in Informatics (ALGI)  2020.9 

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    Event date: 2020.9

    Language:English  

    Country:Japan  

    Other Link: https://sites.google.com/site/algimeeting/home/31/program

  • Specification and Verification of Invariant Properties of Transition Systems Invited International conference

    Daniel Găină

    Working Formal Methods Symposium (FROM 2017)  2017.7 

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    Event date: 2020.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Bucharest   Country:Romania  

    Other Link: http://unibuc.ro/~conference/from2017/#2

  • Horn Clauses in Hybrid-Dynamic First-Order Logic

    Daniel Găină

    The 15th Theorem Proving and Provers meeting (TPP 2019)  2019.11 

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    Event date: 2019.11

    Language:English  

    Venue:National Institute of Informatics   Country:Japan  

    We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems.As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are common to hybrid logics and to dynamic logics.This provides certain key advantages for dealing with reconfigurable systems, such as: (a) a signature of nominals, including operation and relation symbols, that allows references to specific possible worlds / system configurations – as in the case of hybrid logics; (b) distinguished signatures of rigid and flexible symbols, where the rigid symbols are interpreted uniformly across possible worlds; this supports a rigid form of quantification, which ensures that variables have the same interpretation regardless of the possible world where they are evaluated; (c) hybrid terms, which increase the expressive power of the logic in the context of rigid symbols; and (d) modal operators over dynamic-logic actions, which are defined as regular expressions over binary nominal relations. We then study Horn clauses in this hybrid-dynamic logic, and develop a series of results that lead to an initial-semantics theorem for arbitrary sets of clauses.This shows that a significant fragment of hybrid-dynamic first-order logic has good computational properties, and can serve as a basis for defining executable languages for reconfigurable systems.

    Other Link: https://akihisayamada.github.io/tpp2019/

  • Birkhoff Completeness for Hybrid-Dynamic First-Order Logic

    Daniel Găină

    The 18th Logic and Computation Seminar  2019.11 

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    Event date: 2019.11

    Language:English  

    Venue:Nishijin Plaza, Multi-purpse Room(2-16-23 Nishijin, Sawara-ku, Fukuoka-shi)   Country:Japan  

    Hybrid-dynamic first-order logic is a kind of modal logic obtained by enriching many-sorted first-order logic with features that are common to hybrid and to dynamic logics. This provides us with a logical system with an increased expressive power thanks to a number of distinctive attributes:
    (a) first, the possible worlds of Kripke structures, as well as the nominals used to identify them, are endowed with an algebraic structure;
    (b) second, we distinguish between rigid symbols, which have the same interpretation across possible worlds — and thus provide support for the standard rigid quantification in modal logic — and flexible symbols, whose interpretation may vary;
    (c) third, we use modal operators over dynamic-logic actions, which are defined as regular expressions over binary nominal relations.
    In this context, we propose a general notion of hybrid-dynamic Horn clause and develop a proof calculus for the Horn-clause fragment of hybrid-dynamic first-order logic. We investigate soundness and compactness properties for the syntactic entailment system that corresponds to this proof calculus, and prove a Birkhoff-completeness result for hybrid-dynamic first-order logic.

    Other Link: https://lcseminar.wordpress.com/2019/11/12/lcseminar18/

  • Mathematical structures for developing reconfigurable systems International conference

    Daniel Găină

    La Trobe - Kyushy Joint Seminar on Mathematics for Industry  2017.5 

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    Event date: 2017.5

    Language:English  

    Country:Japan  

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Works

  • Transition Algebra Theorem Prover

    Daniel Găină, Ionuţ Ţuţu, Adrián Riesco, Go Hashimoto

    2023.10

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    Expressivity and executability are two highly desirable yet often clashing features of formal specification languages. One empowers the users of such languages to capture a broad range of applications in a natural, convenient manner, while the other is essential for rapid prototyping, as it provides immediate feedback on the functional behavior of the systems specified in this way. In general, neither can be fully achieved without sacrificing the other. This has led to modern specification languages that either enjoy the expressive power of full first-order logics or attempt to maximize expressivity while preserving executability within the bounds of some Horn-clause fragment. We have shown that, for formal verification purposes, executability and expressivity may still coexist. To this end, we present a theorem prover that combines executable specifications written in Maude—utilized both in system specification and for conducting proofs—with the expressivity of transition algebra, a logical system built by enhancing many-sorted first-order logic with features of dynamic logic. To illustrate the approach and the benefits of having an executable basis for formal verification, we explored Robin Milner’s calculus of communicating systems—a process calculus that enables syntactic descriptions of concurrent systems to be written, manipulated, and analyzed.

  • Constructor-based Interractive Theorem Prover

    Daniel Găină, Ionuţ Ţuţu, Adrián Riesco

    2018.12

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    The Constructor-based Inductive Theorem Prover (CITP) is a proof management tool built on top of a variation of conditional equational logic enhanced with many modern features.
    The tool consists of two parts:
    - the core, which implements proof tactics, and
    - the user interface, which implements the parser, displays the results, and defines commands through which users can interact with the tool.

Professional Memberships

  • Mathematical Society of Japan

Academic Activities

  • Program Committee member International contribution

    International Workshop on Formal Analysis and Verification of Post-Quantum Cryptographic Protocols FAVPQC 2022  ( Madrid Spain ) 2022.10

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    Type:Competition, symposium, etc. 

  • Screening of academic papers

    Role(s): Peer review

    2022

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    Type:Peer review 

    Proceedings of International Conference Number of peer-reviewed papers:1

    Proceedings of domestic conference Number of peer-reviewed papers:3

  • Screening of academic papers

    Role(s): Peer review

    2021

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    Type:Peer review 

    Proceedings of International Conference Number of peer-reviewed papers:1

    Proceedings of domestic conference Number of peer-reviewed papers:3

  • Programme Committee member International contribution

    8th Conference on Algebra and Coalgebra in Computer Science CALCO 2019  ( London UnitedKingdom ) 2019.6

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    Type:Competition, symposium, etc. 

  • Screening of academic papers

    Role(s): Peer review

    2019

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:1

    Proceedings of International Conference Number of peer-reviewed papers:3

    Proceedings of domestic conference Number of peer-reviewed papers:3

Research Projects

  • A theorem prover for the correct development of reconfigurable systems International coauthorship

    2023.4 - 2027.4

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    Authorship:Principal investigator 

  • A theorem prover for the correct development of reconfigurable systems

    Grant number:60050  2023 - 2026

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • Mathematical foundations for the reconfiguration paradigm International coauthorship

    2020.4 - 2024.3

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    Authorship:Principal investigator 

  • Mathematical foundations for the reconfiguration paradigm

    Grant number:12030  2020 - 2024

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • The relationship between gaining expressive power in extending first-order logics and losing 'control' over the extension International coauthorship

    2018.4 - 2021.3

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    Authorship:Principal investigator 

    The purpose of this project is to complete the work started by Lindstrom on the expressivity of first-order logic by making his result not only syntactic-free but also semantic-free in the spirit of abstract model theory.

Educational Activities

  • I have taught a variety of applied mathematical subjects such as algebraic specification, model theoretic topics for the design of specification and verification languages, or term rewriting. I organize lectures in collaboration with other universities such as La Trobe University. I also supervise graduate research students.

Class subject

  • 情報数学特論1

    2024.10 - 2025.3   Second semester

  • 数理科学特論19

    2024.4 - 2024.9   First semester

  • MMA数学特論II

    2024.4 - 2024.9   First semester

  • 数学共創概論Ⅱ

    2023.10 - 2024.3   Second semester

  • 機能数理学概論Ⅰ

    2023.10 - 2024.3   Second semester

  • MMA数学特論II

    2023.10 - 2024.3   Second semester

  • 数理科学特論19

    2023.10 - 2024.3   Second semester

  • 数学共創概論Ⅱ

    2023.10 - 2024.3   Second semester

  • 機能数理学概論Ⅰ

    2023.10 - 2024.3   Second semester

  • MMA数学特論II

    2023.10 - 2024.3   Second semester

  • 数理科学特論19

    2023.10 - 2024.3   Second semester

  • 数学創発モデリング

    2023.4 - 2024.3   Full year

  • 数学創発モデリング

    2023.4 - 2024.3   Full year

  • 計算数理学Ⅰ

    2023.4 - 2023.9   First semester

  • ルベーグ積分

    2023.4 - 2023.9   First semester

  • 計算数理学Ⅰ

    2023.4 - 2023.9   First semester

  • ルベーグ積分

    2023.4 - 2023.9   First semester

  • Functional Mathematics I

    2022.10 - 2023.3   Second semester

  • Functional Mathematics I

    2022.10 - 2023.3   Second semester

  • 数学共創概論Ⅱ

    2022.10 - 2023.3   Second semester

  • 機能数理学概論Ⅰ

    2022.10 - 2023.3   Second semester

  • MMA数学特論II

    2022.10 - 2023.3   Second semester

  • 数理科学特論19

    2022.10 - 2023.3   Second semester

  • 数学共創モデリング

    2022.4 - 2023.3   Full year

  • 数学共創モデリング

    2022.4 - 2023.3   Full year

  • Topics in Computational Mathematics I

    2022.4 - 2022.9   First semester

  • Topics in Computational Mathematics I

    2022.4 - 2022.9   First semester

  • Topics in Computational Mathematics I

    2022.4 - 2022.9   First semester

  • 計算数理学Ⅰ

    2022.4 - 2022.9   First semester

  • 計算数理学Ⅰ

    2022.4 - 2022.9   First semester

  • 応用数学A

    2022.4 - 2022.9   First semester

  • 機能数理学概論Ⅰ

    2021.10 - 2022.3   Second semester

  • MMA数学特論II

    2021.10 - 2022.3   Second semester

  • 数理科学特論19

    2021.10 - 2022.3   Second semester

  • 機能数理学概論Ⅰ

    2021.10 - 2022.3   Second semester

  • MMA数学特論II

    2021.10 - 2022.3   Second semester

  • 数理科学特論19

    2021.10 - 2022.3   Second semester

  • 機能数理学概論Ⅰ

    2021.10 - 2022.3   Second semester

  • MMA数学特論II

    2021.10 - 2022.3   Second semester

  • 数理科学特論19

    2021.10 - 2022.3   Second semester

  • 計算数理学Ⅰ

    2021.4 - 2021.9   First semester

  • 応用数学A

    2021.4 - 2021.9   First semester

  • 計算数理学Ⅰ

    2021.4 - 2021.9   First semester

  • 応用数学A

    2021.4 - 2021.9   First semester

  • 計算数理学Ⅰ

    2021.4 - 2021.9   First semester

  • 応用数学A

    2021.4 - 2021.9   First semester

  • [M2]Topics in Computational Mathematics I

    2021.4 - 2021.9   First semester

  • [M2]計算数理学Ⅰ

    2021.4 - 2021.9   First semester

  • MMA数学特論Ⅱ

    2020.10 - 2021.3   Second semester

  • 数理科学特論19

    2020.10 - 2021.3   Second semester

  • 機能数理学概論Ⅰ

    2020.4 - 2020.9   First semester

  • 応用数学Ⅱ

    2020.4 - 2020.9   First semester

  • MMA数学入門

    2020.4 - 2020.9   First semester

  • MMA数学入門

    2020.4 - 2020.9   First semester

  • MMA数学入門

    2020.4 - 2020.9   First semester

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Other educational activity and Special note

  • 2023  Coaching of Students' Association  I am involved in organizing a soccer circle/club open to both international and Japanese students

Outline of Social Contribution and International Cooperation activities

  • I am involved in research collaborations with European and Australian academics as well as with Japanese researchers.
    I organize an online seminar for the development of a software tool for the specification and verification of reconfigurable systems. My collaborators for this project are Adrian Riesco (Complutense University of Madrid) and Ionut Tutu (Institute of Mathematics of the Romanian Academy).
    I work with Tomasz Kowalski (Jagiellonian University, Poland) and Guillermo Badia (The University of Queensland) on a project where we study the relationship between gaining expressive power in extending first-order logics and losing 'control' over the extension.
    I am involved in the organization of joint research seminars with Mathematics and Statistics Department of La Trobe University.

Activities contributing to policy formation, academic promotion, etc.

  • 2018.2   Co-organized by the Institute of Mathematics for Industry at Kyushu University and La Trobe University

    Main organizer of the international “Workshop on Logic, Algebra and Category Theory”, Melbourne, February 12-16, 2018

Travel Abroad

  • 2022.8 - 2022.9

    Staying countory name 1:Romania   Staying institution name 1:Institute of Mathematics of the Romanian Academy

  • 2022.8

    Staying countory name 1:France   Staying institution name 1:The french laboratory for research and innovation in digital science and technology (IRISA)