{"title":"Principles of Superdeduction","authors":"Paul Brauner, C. Houtmann, C. Kirchner","doi":"10.1109/LICS.2007.37","DOIUrl":"https://doi.org/10.1109/LICS.2007.37","url":null,"abstract":"In predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in the theory in a uniform way. Introduced ten years ago, deduction modulo allows us to make use of the computational part of the theory Th for true computations modulo which deductions are performed. Focusing on the sequent calculus, this paper presents and studies the dual concept where the theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. We call such a new deduction system \"superdeduction \". We introduce a proof-term language and a cut-elimination procedure both based on Christian Urban's work on classical sequent calculus. Strong normalisation is proven under appropriate and natural hypothesis, therefore ensuring the consistency of the embedded theory and of the deduction system. The proofs obtained in such a new system are much closer to the human intuition and practice. We consequently sketch how superdeduction along with deduction modulo can be used to ground the formal foundations of new extendible proof assistants like lemuridae, our prototypal implementation of superdeduction modulo.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123546282","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}
{"title":"A New Efficient Simulation Equivalence Algorithm","authors":"Francesco Ranzato, Francesco Tapparo","doi":"10.1109/LICS.2007.8","DOIUrl":"https://doi.org/10.1109/LICS.2007.8","url":null,"abstract":"It is well known that simulation equivalence is an appropriate abstraction to be used in model checking because it strongly preserves ACTL* and provides a better space reduction than bisimulation equivalence. However, computing simulation equivalence is harder than computing bisimulation equivalence. A number of algorithms for computing simulation equivalence exist. Let Sigma denote the state space, rarr the transition relation and Psim the partition of Sigma induced by simulation equivalence. The algorithms by Henzinger, Henzinger, Kopke and by Bloom and Paige run in O(|Sigma||rarr|)-time and, as far as time-complexity is concerned, they are the best available algorithms. However, these algorithms have the drawback of a quadratic space complexity that is bounded from below by Omega(|Sigma|2). The algorithm by Gentilini, Piazza, Policriti appears to be the best algorithm when both time and space complexities are taken into account. Gentilini et al.'s algorithm runs in O(|Psim|2|rarr|)-time while the space complexity is in O(|Psim|2 + |Sigma| log(|Psim|)). We present here a new efficient simulation equivalence algorithm that is obtained as a modification of Henzinger et al.'s algorithm and whose correctness is based on some techniques used in recent applications of abstract interpretation to model checking. Our algorithm runs in O(|Psim||rarr|)-time and O(|Psim||Sigma|)-space. Thus, while retaining a space complexity which is lower than quadratic, our algorithm improves the best known time bound.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123616599","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}
{"title":"Limits of Multi-Discounted Markov Decision Processes","authors":"H. Gimbert, Wieslaw Zielonka","doi":"10.1109/LICS.2007.28","DOIUrl":"https://doi.org/10.1109/LICS.2007.28","url":null,"abstract":"Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. The payoff received by the controller can be evaluated in different ways, depending on the payoff function the MDP is equipped with. For example a mean-payoff function evaluates average performance, whereas a discounted payoff function gives more weights to earlier performance by means of a discount factor. Another well-known example is the parity payoff function which is used to encode logical specifications. Surprisingly, parity and mean-payoff MDPs share two non-trivial properties: they both have pure stationary optimal strategies and they both are approximable by discounted MDPs with multiple discount factors (multi- discounted MDPs). In this paper we unify and generalize these results. We introduce a new class of payoff functions called the priority weighted payoff functions, which are generalization of both parity and mean-payoff functions. We prove that priority weighted MDPs admit optimal strategies that are pure and stationary, and that the priority weighted value of an MDP is the limit of the multi-discounted value when discount factors tend to 0 simultaneously at various speeds.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124965638","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}
{"title":"Environmental Bisimulations for Higher-Order Languages","authors":"D. Sangiorgi, N. Kobayashi, Eijiro Sumii","doi":"10.1145/1889997.1890002","DOIUrl":"https://doi.org/10.1145/1889997.1890002","url":null,"abstract":"Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with \"up-to context\" techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure lambda-calculi (call-by-name and call-by-value), call-by-value lambda-calculus with higher-order store, and then higher-order pi-calculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe's for proving congruence. It also scales from the pure lambda-calculi to the richer calculi with simple congruence proofs.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129258442","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}
L. D. Alfaro, R. Majumdar, Vishwanath Raman, Marielle Stoelinga
{"title":"Game Relations and Metrics","authors":"L. D. Alfaro, R. Majumdar, Vishwanath Raman, Marielle Stoelinga","doi":"10.1109/LICS.2007.22","DOIUrl":"https://doi.org/10.1109/LICS.2007.22","url":null,"abstract":"We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., \"reach a target state\"), the question of winning is thus a probabilistic one: \"what is the maximal probability of winning from a given state?\". On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state \"similarity\". We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose goals are expressed in the quantitative mu-calculus. The quantitative mu- calculus can express a large set of goals, including reachability, safety, and omega-regular properties. Thus, we claim that our relations and metrics provide the canonical extensions to games, of the classical notion of bisimulation for transition systems. We develop our results both for equivalences and metrics, which generalize bisimulation, and for asymmetrical versions, which generalize simulation.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115417633","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}
{"title":"Static Name Control for FreshML","authors":"F. Pottier","doi":"10.1109/LICS.2007.44","DOIUrl":"https://doi.org/10.1109/LICS.2007.44","url":null,"abstract":"FreshML extends ML with constructs for declaring and manipulating abstract syntax trees that involve names and statically scoped binders. It is impure: name generation is an observable side effect. In practice, this means that FreshML allows writing programs that create fresh names and unintentionally fail to bind them. Following in the steps of early work by Pitts and Gabbay, this paper defines Pure FreshML, a subset of FreshML equipped with a static proof system that guarantees purity. Pure FreshML relies on a rich binding specification language, on user-provided assertions, expressed in a logic that allows reasoning about values and about the names that they contain, and on a conservative, automatic decision procedure for this logic. It is argued that pure FreshML can express non-trivial syntax-manipulating algorithms.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123041681","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}
{"title":"Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements","authors":"Andreas Abel, T. Coquand, P. Dybjer","doi":"10.1109/LICS.2007.33","DOIUrl":"https://doi.org/10.1109/LICS.2007.33","url":null,"abstract":"The decidability of equality is proved for Martin-Lof type theory with a universe a la Russell and typed beta-eta- equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123501947","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}
{"title":"Local Action and Abstract Separation Logic","authors":"Cristiano Calcagno, P. O'Hearn, Hongseok Yang","doi":"10.1109/LICS.2007.30","DOIUrl":"https://doi.org/10.1109/LICS.2007.30","url":null,"abstract":"Separation logic is an extension of Hoare's logic which supports a local way of reasoning about programs that mutate memory. We present a study of the semantic structures lying behind the logic. The core idea is of a local action, a state transformer that mutates the state in a local way. We formulate local actions for a class of models called separation algebras, abstracting from the RAM and other specific concrete models used in work on separation logic. Local actions provide a semantics for a generalized form of (sequential) separation logic. We also show that our conditions on local actions allow a general soundness proof for a separation logic for concurrency, interpreted over arbitrary separation algebras.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115803990","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}
{"title":"Complete Sequent Calculi for Induction and Infinite Descent","authors":"J. Brotherston, A. Simpson","doi":"10.1109/LICS.2007.16","DOIUrl":"https://doi.org/10.1109/LICS.2007.16","url":null,"abstract":"This paper compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system supports traditional proof by induction, with induction rules formulated as sequent rules for introducing inductively defined predicates on the left of sequents. We show this system to be cut-free complete with respect to a natural class of Henkin models; the eliminability of cut follows as a corollary. The second system uses infinite (non-well-founded) proofs to represent arguments by infinite descent. In this system, the left rules for inductively defined predicates are simple case-split rules, and an infinitary, global condition on proof trees is required to ensure soundness. We show this system to be cut-free complete with respect to standard models, and again infer the eliminability of cut. The second infinitary system is unsuitable for formal reasoning. However, it has a natural restriction to proofs given by regular trees, i.e. to those proofs representable by finite graphs. This restricted \"cyclic\" system subsumes the first system for proof by induction. We conjecture that the two systems are in fact equivalent, i.e., that proof by induction is equivalent to regular proof by infinite descent.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129419425","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}
{"title":"Infinite sets that admit fast exhaustive search","authors":"M. Escardó","doi":"10.1109/LICS.2007.25","DOIUrl":"https://doi.org/10.1109/LICS.2007.25","url":null,"abstract":"Perhaps surprisingly, there are infinite sets that admit mechanical exhaustive search in finite time. We investigate three related questions: What kinds of infinite sets admit mechanical exhaustive search in finite time? How do we systematically build such sets? How fast can exhaustive search over infinite sets be performed?","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114169053","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}