ACM Transactions on Computational Logic (TOCL)最新文献

{"title":"α β-Relations and the Actual Meaning of α-Renaming","authors":"Michele Basaldella","doi":"10.1145/3426471","DOIUrl":"https://doi.org/10.1145/3426471","url":null,"abstract":"In this work we provide an alternative, and equivalent, formulation of the concept of λ-theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We call α β-relations our alternative versions of λ-theories. We also clarify the actual role of α-renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of α-renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not α-renaming. The article also has a survey character.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128914657","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":"Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints","authors":"B. Bogaerts, L. Cruz-Filipe","doi":"10.1145/3430750","DOIUrl":"https://doi.org/10.1145/3430750","url":null,"abstract":"Approximation fixpoint theory (AFT) is an algebraic study of fixpoints of lattice operators that unifies various knowledge representation formalisms. In AFT, stratification of operators has been studied, essentially resulting in a theory that specifies when certain types of fixpoints can be computed stratum per stratum. Recently, novel types of fixpoints related to groundedness have been introduced in AFT. In this article, we study how those fixpoints behave under stratified operators. One recent application domain of AFT is the field of active integrity constraints (AICs). We apply our extended stratification theory to AICs and find that existing notions of stratification in AICs are covered by this general algebraic definition of stratification. As a result, we obtain stratification results for a large variety of semantics for AICs.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130487950","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":"Satisfiability Problems on Sums of Kripke Frames","authors":"I. Shapirovsky","doi":"10.1145/3508068","DOIUrl":"https://doi.org/10.1145/3508068","url":null,"abstract":"We consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. In many cases, the modal logic of sums inherits the finite model property and decidability from the modal logic of summands [Babenyshev and Rybakov 2010; Shapirovsky 2018]. In this paper we show that, under a general condition, the satisfiability problem on sums is polynomial space Turing reducible to the satisfiability problem on summands. In particular, for many modal logics decidability in PSpace is an immediate corollary from the semantic characterization of the logic.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"63 Suppl 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128163518","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":"Beyond Uniform Equivalence between Answer-set Programs","authors":"J. Oetsch, M. Seidl, H. Tompits, S. Woltran","doi":"10.1145/3422361","DOIUrl":"https://doi.org/10.1145/3422361","url":null,"abstract":"This article deals with advanced notions of equivalence between nonmonotonic logic programs under the answer-set semantics, a topic of considerable interest, because such notions form the basis for program verification and are useful for program optimisation, debugging, and modular programming. In fact, there is extensive research in answer-set programming (ASP) dealing with different notions of equivalence between programs. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joined with an arbitrary set of facts. In this article, we study a family of more fine-grained versions of uniform equivalence, viz. relativised uniform equivalence with projection, which extends standard uniform equivalence in terms of two additional parameters: one for specifying the input alphabet and one for specifying the output alphabet for programs. In particular, the second parameter is used for projecting answer sets to a set of designated output atoms. Answer-set projection, in particular, allows to compare programs that make use of different auxiliary atoms, which is important for practical programming aspects. We introduce novel semantic characterisations for the program correspondence problems under consideration and analyse their computational complexity. In the general case, deciding these problems lies on the third level of the polynomial hierarchy. Therefore, this task cannot be efficiently reduced to propositional answer-set programs itself (under the usual complexity-theoretic assumptions). However, reductions to quantified Boolean formulas (QBFs) are feasible. Indeed, we provide efficient (in fact, linear-time constructible) reductions to QBFs and discuss simplifications for certain special cases. These QBF reductions yield the basis for a prototype implementation, the system cc ⊤, for deciding correspondence problems by using off-the-shelf QBF solvers. We discuss an application of cc ⊤ for verifying the correctness of solutions by students drawn from a laboratory course on logic programming and knowledge representation at the Technische Universität Wien, employing relativised uniform equivalence with projection as the underlying program correspondence notion.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130333949","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":"Logics with Multiteam Semantics","authors":"E. Grädel, Richard Wilke","doi":"10.1145/3487579","DOIUrl":"https://doi.org/10.1145/3487579","url":null,"abstract":"Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters, but being based on sets, it does not take into account multiple occurrences of data values. It is therefore insufficient in scenarios where such multiplicities matter, in particular for reasoning about probabilities and statistical independencies. Therefore, an extension from teams to multiteams (i.e. multisets of assignments) has been proposed by several authors. In this paper we aim at a systematic development of logics of dependence and independence based on multiteam semantics. We study atomic dependency properties of finite multiteams and discuss the appropriate meaning of logical operators to extend the atomic dependencies to full-fledged logics for reasoning about dependence properties in a multiteam setting. We explore properties and expressive power of a wide spectrum of different multiteam logics and compare them to second-order logic and to logics with team semantics. In many cases the results resemble what is known in team semantics, but there are also interesting differences. While in team semantics, the combination of inclusion and exclusion dependencies leads to a logic with the full power of both independence logic and existential second-order logic, independence properties of multiteams are not definable by any combination of properties that are downwards closed or union closed and thus are strictly more powerful than inclusion-exclusion logic. We also study the relationship of logics with multiteam semantics with existential second-order logic for a specific class of metafinite structures. It turns out that inclusion-exclusion logic can be characterised in a precise sense by the Presburger fragment of this logic, but for capturing independence, we need to go beyond it and add some form of multiplication. Finally, we also consider multiteams with weights in the reals and study the expressive power of formulae by means of topological properties.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123266891","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":"Model Checking a Logic for True Concurrency","authors":"Paolo Baldan, Tommaso Padoan","doi":"10.1145/3412853","DOIUrl":"https://doi.org/10.1145/3412853","url":null,"abstract":"We study the model-checking problem for a logic for true concurrency, whose formulae predicate about events in computations and their causal dependencies. The logic, which represents the logical counterpart of history-preserving bisimilarity, is naturally interpreted over event structures or any formalism that can be given a causal semantics, like Petri nets. It includes least and greatest fixpoint operators and thus it can express properties of infinite computations. Since the event structure associated with a system is typically infinite (even if the system is finite state), already the decidability of model-checking is non-trivial. We first develop a local model-checking technique based on a tableau system, for which, over a class of event structures satisfying a suitable regularity condition, referred to as strong regularity, we prove termination, soundness, and completeness. The tableau system allows for a clean and intuitive proof of decidability, but a direct implementation of the procedure can be extremely inefficient. For easing the development of a more efficient model-checking technique, we move to an automata-theoretic framework. Given a formula and a strongly regular event structure, we show how to construct a parity tree automaton whose language is non-empty if and only if the event structure satisfies the formula. The automaton is usually infinite. We discuss how it can be quotiented to an equivalent finite automaton, where emptiness can be checked effectively. To show the applicability of the approach, we discuss how it instantiates to finite safe Petri nets, providing also a corresponding proof-of-concept model-checking tool.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134435408","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":"Applying Visible Strong Equivalence in Answer-Set Program Transformations","authors":"J. Bomanson, T. Janhunen, I. Niemelä","doi":"10.1145/3412854","DOIUrl":"https://doi.org/10.1145/3412854","url":null,"abstract":"Strong equivalence is one of the basic notions of equivalence that have been proposed for logic programs subject to the answer-set semantics. In this article, we propose a new generalization of strong equivalence (SE) that takes the visibility of atoms into account and we characterize it in terms of appropriately revised SE-models. Our design resembles (relativized) strong equivalence but is substantially different due to adopting a strict one-to-one correspondence of models from the notion of visible equivalence. We additionally tailor the characterization for more convenient use with positive programs and provide formal tools to exploit the tailored version also in the case of some programs that use negation. We illustrate the use of visible strong equivalence and the characterizations in showing the correctness of program transformations that make use of atom visibility. Moreover, we present a translation that enables us to automate the task of verifying visible strong equivalence for particular fragments of answer-set programs. We experimentally study the efficiency of verification when the goal is to check whether an extended rule is visibly strongly equivalent to its normalization, i.e., a subprogram expressing the original rule in terms of normal rules only. In the process, we verify the outputs of several real implementations of normalization schemes on a considerable number of input rules.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128153439","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":"Collapsible Pushdown Parity Games","authors":"Christopher H. Broadbent, Arnaud Carayol, M. Hague, A. Murawski, C. Ong, O. Serre","doi":"10.1145/3457214","DOIUrl":"https://doi.org/10.1145/3457214","url":null,"abstract":"This article studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely, those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126707116","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":"Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics","authors":"C. Kupke, D. Pattinson, Lutz Schröder","doi":"10.1145/3501300","DOIUrl":"https://doi.org/10.1145/3501300","url":null,"abstract":"We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124359656","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":"Principles of KLM-style Defeasible Description Logics","authors":"K. Britz, G. Casini, T. Meyer, Kodylan Moodley, U. Sattler, I. Varzinczak","doi":"10.1145/3420258","DOIUrl":"https://doi.org/10.1145/3420258","url":null,"abstract":"The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121329830","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}