A novel countermodel-producing decision procedure that applies to several multi-modal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure, it is argued that multi-modal variants of several classical and intuitionistic logics including K, T, K4, S4 and their combinations with D are decidable and have the finite model property. At least in the intuitionistic multi-modal case, the decidability results are new. It is further shown that the countermodels produced by the procedure, starting from a set of hypotheses and no goals, characterize the atomic formulas provable from the hypotheses.
{"title":"Countermodels from Sequent Calculi in Multi-Modal Logics","authors":"D. Garg, Valerio Genovese, Sara Negri","doi":"10.1109/LICS.2012.42","DOIUrl":"https://doi.org/10.1109/LICS.2012.42","url":null,"abstract":"A novel countermodel-producing decision procedure that applies to several multi-modal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure, it is argued that multi-modal variants of several classical and intuitionistic logics including K, T, K4, S4 and their combinations with D are decidable and have the finite model property. At least in the intuitionistic multi-modal case, the decidability results are new. It is further shown that the countermodels produced by the procedure, starting from a set of hypotheses and no goals, characterize the atomic formulas provable from the hypotheses.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121054752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Linear authorization logics (LAL) are logics based on linear logic that can be used for modeling effect-based authentication policies. LAL has been used in the context of the Proof-Carrying Authorization framework, where formal proofs are constructed in order for a principal to gain access to some resource elsewhere. This paper investigates the complexity of the provability problem, that is, determining whether a linear authorization logic formula is provable or not. We show that the multiplicative propositional fragment of LAL is already undecidable in the presence of two principals. On the other hand, we also identify a first-order fragment of LAL for which provability is PSPACE-complete. Finally, we argue by example that the latter fragment is natural and can be used in practice.
{"title":"On the Complexity of Linear Authorization Logics","authors":"Vivek Nigam","doi":"10.1109/LICS.2012.61","DOIUrl":"https://doi.org/10.1109/LICS.2012.61","url":null,"abstract":"Linear authorization logics (LAL) are logics based on linear logic that can be used for modeling effect-based authentication policies. LAL has been used in the context of the Proof-Carrying Authorization framework, where formal proofs are constructed in order for a principal to gain access to some resource elsewhere. This paper investigates the complexity of the provability problem, that is, determining whether a linear authorization logic formula is provable or not. We show that the multiplicative propositional fragment of LAL is already undecidable in the presence of two principals. On the other hand, we also identify a first-order fragment of LAL for which provability is PSPACE-complete. Finally, we argue by example that the latter fragment is natural and can be used in practice.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130922473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players' objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrent-game semantics for predicate calculus is provided as an illustration.
{"title":"The Winning Ways of Concurrent Games","authors":"P. Clairambault, J. Gutierrez, G. Winskel","doi":"10.1109/LICS.2012.34","DOIUrl":"https://doi.org/10.1109/LICS.2012.34","url":null,"abstract":"A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players' objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrent-game semantics for predicate calculus is provided as an illustration.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132906391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Model checking-deciding if a logical sentence holds on a structure-is a basic computational task that is well-known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.
{"title":"Decomposing Quantified Conjunctive (or Disjunctive) Formulas","authors":"Hubie Chen, V. Dalmau","doi":"10.1109/LICS.2012.31","DOIUrl":"https://doi.org/10.1109/LICS.2012.31","url":null,"abstract":"Model checking-deciding if a logical sentence holds on a structure-is a basic computational task that is well-known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132562257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. This is a brief survey of differential dynamic logic for specifying and verifying properties of hybrid systems. We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems. We study differential invariants, i.e., induction principles for differential equations. We briefly survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logic has been implemented in automatic and interactive theorem provers and has been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics, and analogue electrical circuits.
{"title":"Logics of Dynamical Systems","authors":"André Platzer","doi":"10.1109/LICS.2012.13","DOIUrl":"https://doi.org/10.1109/LICS.2012.13","url":null,"abstract":"We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. This is a brief survey of differential dynamic logic for specifying and verifying properties of hybrid systems. We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems. We study differential invariants, i.e., induction principles for differential equations. We briefly survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logic has been implemented in automatic and interactive theorem provers and has been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics, and analogue electrical circuits.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121867640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.
{"title":"The HOM Problem is EXPTIME-Complete","authors":"Carles Creus, Adrià Gascón, Guillem Godoy, Lander Ramos","doi":"10.1109/LICS.2012.36","DOIUrl":"https://doi.org/10.1109/LICS.2012.36","url":null,"abstract":"The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131709794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martin-Löf's type theory has strong existential elimination (dependent sum type) that allows to prove the full axiom of choice. However the theory is intuitionistic. We give a condition on strong existential elimination that makes it computationally compatible with classical logic. With this restriction, we lose the full axiom of choice but, thanks to a lazily-evaluated coinductive representation of quantification, we are still able to constructively prove the axiom of countable choice, the axiom of dependent choice, and a form of bar induction in ways that make each of them computationally compatible with classical logic.
{"title":"A Constructive Proof of Dependent Choice, Compatible with Classical Logic","authors":"Hugo Herbelin","doi":"10.1109/LICS.2012.47","DOIUrl":"https://doi.org/10.1109/LICS.2012.47","url":null,"abstract":"Martin-Löf's type theory has strong existential elimination (dependent sum type) that allows to prove the full axiom of choice. However the theory is intuitionistic. We give a condition on strong existential elimination that makes it computationally compatible with classical logic. With this restriction, we lose the full axiom of choice but, thanks to a lazily-evaluated coinductive representation of quantification, we are still able to constructively prove the axiom of countable choice, the axiom of dependent choice, and a form of bar induction in ways that make each of them computationally compatible with classical logic.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131260791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces HOpiPn, the higher-order pi-calculus with passivation and name creation, and develops an equivalence theory for this calculus. Passivation [Schmitt and Stefani] is a language construct that elegantly models higher-order distributed behaviours like failure, migration, or duplication (e.g. when a running process or virtual machine is copied), and name creation consists in generating a fresh name instead of hiding one. Combined with higher-order distribution, name creation leads to different semantics from name hiding, and is closer to implementations of distributed systems. We define for this new calculus a theory of sound and complete environmental bisimulation to prove reduction-closed barbed equivalence and (a reasonable form of) congruence. We furthermore define environmental simulations to prove behavioural approximation, and use these theories to show non-trivial examples of equivalence or approximation. Those examples could not be proven with previous theories, which were either unsound or incomplete under the presence of process duplication and name restriction, or else required universal quantification over general contexts.
{"title":"A Higher-Order Distributed Calculus with Name Creation","authors":"Adrien Piérard, Eijiro Sumii","doi":"10.1109/LICS.2012.63","DOIUrl":"https://doi.org/10.1109/LICS.2012.63","url":null,"abstract":"This paper introduces HOpiPn, the higher-order pi-calculus with passivation and name creation, and develops an equivalence theory for this calculus. Passivation [Schmitt and Stefani] is a language construct that elegantly models higher-order distributed behaviours like failure, migration, or duplication (e.g. when a running process or virtual machine is copied), and name creation consists in generating a fresh name instead of hiding one. Combined with higher-order distribution, name creation leads to different semantics from name hiding, and is closer to implementations of distributed systems. We define for this new calculus a theory of sound and complete environmental bisimulation to prove reduction-closed barbed equivalence and (a reasonable form of) congruence. We furthermore define environmental simulations to prove behavioural approximation, and use these theories to show non-trivial examples of equivalence or approximation. Those examples could not be proven with previous theories, which were either unsound or incomplete under the presence of process duplication and name restriction, or else required universal quantification over general contexts.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"124 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133874359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary form only given. I use a revised, more robust, notion of computability to answer bothersome questions that are not even easy to ask with any clarity.
{"title":"Turing's Password: What Internet Cannot Leak","authors":"L. Levin","doi":"10.1109/LICS.2012.11","DOIUrl":"https://doi.org/10.1109/LICS.2012.11","url":null,"abstract":"Summary form only given. I use a revised, more robust, notion of computability to answer bothersome questions that are not even easy to ask with any clarity.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133757846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We demonstrate how the Hyland-Tan double glueing construction produces a fully complete model of the unit-free multiplicative fragment of Linear Logic when applied to any of a large family of degenerative ones. This process explains as special cases a number of such models which appear in the literature. In order to achieve this result, we make use of a tensor calculus for compact closed categories with finite biproducts. We show how the combinatorial properties required for a fully complete model are obtained by the construction adding to those already available from the original category.
{"title":"Constructing Fully Complete Models for Multiplicative Linear Logic","authors":"A. Schalk, Hugh P. Steele","doi":"10.1109/LICS.2012.67","DOIUrl":"https://doi.org/10.1109/LICS.2012.67","url":null,"abstract":"We demonstrate how the Hyland-Tan double glueing construction produces a fully complete model of the unit-free multiplicative fragment of Linear Logic when applied to any of a large family of degenerative ones. This process explains as special cases a number of such models which appear in the literature. In order to achieve this result, we make use of a tensor calculus for compact closed categories with finite biproducts. We show how the combinatorial properties required for a fully complete model are obtained by the construction adding to those already available from the original category.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116264895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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