ACM Transactions on Computational Logic最新文献

{"title":"Local Search For Satisfiability Modulo Integer Arithmetic Theories","authors":"Shaowei Cai, Bohan Li, Xindi Zhang","doi":"https://dl.acm.org/doi/10.1145/3597495","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3597495","url":null,"abstract":"<p>Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first-order theories. In this article, we focus on Satisfiablity Modulo Integer Arithmetic, which is referred to as SMT(IA), including both linear and non-linear integer arithmetic theories. Dominant approaches to SMT rely on calling a CDCL-based SAT solver, either in a lazy or eager flavour. Local search, a competitive approach to solving combinatorial problems including SAT, however, has not been well studied for SMT. We develop the first local-search algorithm for SMT(IA) by directly operating on variables, breaking through the traditional framework. We propose a local-search framework by considering the distinctions between Boolean and integer variables. Moreover, we design a novel operator and scoring functions tailored for integer arithmetic, as well as a two-level operation selection heuristic. Putting these together, we develop a local search SMT(IA) solver called LocalSMT. Experiments are carried out to evaluate LocalSMT on benchmark sets from SMT-LIB. The results show that LocalSMT is competitive and complementary with state-of-the-art SMT solvers, and performs particularly well on those formulae with only integer variables. A simple sequential portfolio with Z3 improves the state-of-the-art on satisfiable benchmark sets from SMT-LIB.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"36 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inputs, Outputs, and Composition in the Logic of Information Flows","authors":"Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den Bussche","doi":"https://dl.acm.org/doi/10.1145/3604553","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3604553","url":null,"abstract":"<p>The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of inputs and outputs of LIF expressions. We study how the two relate and show that our syntactic definition is optimal in a sense that is made precise. The second contribution is a systematic study of the expressive power of sequential composition in LIF. Our results on composition tie in the results on inputs and outputs, and relate LIF to first-order logic (FO) and bounded-variable LIF to bounded-variable FO. </p><p>This paper is the extended version of a paper presented at KR 2020 [2].</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"38 11","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolation Results for Arrays with Length and MaxDiff","authors":"Silvio Ghilardi, Alessandro Gianola, Deepak Kapur, Chiara Naso","doi":"https://dl.acm.org/doi/10.1145/3587161","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3587161","url":null,"abstract":"<p>In this article, we enrich McCarthy’s theory of extensional arrays with a length and a maxdiff operation. As is well-known, some diff operation (i.e., some kind of difference function showing where two unequal arrays differ) is needed to keep interpolants quantifier free in array theories. Our maxdiff operation returns the max index where two arrays differ; thus, it has a univocally determined semantics.</p><p>The length function is a natural complement of such a maxdiff operation and is needed to handle real arrays. Obtaining interpolation results for such a rich theory is a surprisingly hard task. We get such results via a thorough semantic analysis of the models of the theory and of their amalgamation and strong amalgamation properties. The results are modular with respect to the index theory; we show how to convert them into concrete interpolation algorithms via a hierarchical approach realizing a polynomial reduction to interpolation in linear arithmetics endowed with free function symbols.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"37 11","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Decidable Fragment of First Order Modal Logic: Two Variable Term Modal Logic","authors":"Anantha Padmanabha, R. Ramanujam","doi":"https://dl.acm.org/doi/10.1145/3593584","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3593584","url":null,"abstract":"<p><b>First order modal logic (𝖥𝖮𝖬𝖫)</b> is built by extending <b>First Order Logic (𝖥𝖮)</b> with modal operators. A typical formula is of the form (forall x exists y Box P(x,y)). Not only is 𝖥𝖮𝖬𝖫 undecidable, even simple fragments like that of restriction to unary predicate symbols, guarded fragment and two variable fragment, which are all decidable for 𝖥𝖮 become undecidable for 𝖥𝖮𝖬𝖫. In this paper we study <b>Term Modal logic (𝖳𝖬𝖫)</b> which allows modal operators to be indexed by terms. A typical formula is of the form (forall x exists y~Box _x P(x,y)). There is a close correspondence between 𝖳𝖬𝖫 and 𝖥𝖮𝖬𝖫 and we explore this relationship in detail in the paper.</p><p>In contrast to 𝖥𝖮𝖬𝖫, we show that the two variable fragment (without constants, equality) of 𝖳𝖬𝖫 is decidable. Further, we prove that adding a single constant makes the two variable fragment of 𝖳𝖬𝖫 undecidable. On the other hand, when equality is added to the logic, it loses the finite model property.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"38 9","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions","authors":"Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank Wolter","doi":"https://dl.acm.org/doi/10.1145/3597301","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3597301","url":null,"abstract":"<p>The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP reduce potentially hard existence problems to entailment in the underlying logic. Description (and modal) logics with nominals and/or role inclusions do not enjoy the CIP nor the PBDP, but interpolants and explicit definitions have many applications, in particular in concept learning, ontology engineering, and ontology-based data management. In this article we show that, even without Beth and Craig, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as (mathcal {ALCO} ), (mathcal {ALCH} ) and (mathcal {ALCHOI} ) and corresponding hybrid modal logics. However, living without Beth and Craig makes these problems harder than entailment: the existence problems become 2ExpTime-complete in the presence of an ontology or the universal modality, and coNExpTime-complete otherwise. We also analyze explicit definition existence if all symbols (except the one that is defined) are admitted in the definition. In this case the complexity depends on whether one considers individual or concept names. Finally, we consider the problem of computing interpolants and explicit definitions if they exist and turn the complexity upper bound proof into an algorithm computing them, at least for description logics with role inclusions.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"39 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Faster Property Testers in a Variation of the Bounded Degree Model","authors":"Isolde Adler, Polly Fahey","doi":"https://dl.acm.org/doi/10.1145/3584948","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3584948","url":null,"abstract":"<p>Property testing algorithms are highly efficient algorithms that come with probabilistic accuracy guarantees. For a property <i>P</i>, the goal is to distinguish inputs that have <i>P</i> from those that are <i>far</i> from having <i>P</i> with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the <i>distance</i> is measured by the number of edge modifications (additions or deletions) that are necessary to transform a graph into one with property <i>P</i>. Much research has focused on the <i>query complexity</i> of such algorithms, i. e., the number of queries the algorithm makes to the input, but in view of applications, the <i>running time</i> of the algorithm is equally relevant.</p><p>In (Adler, Harwath, STACS 2018), a natural extension of the bounded degree graph model of property testing to relational databases of bounded degree was introduced, and it was shown that on databases of bounded degree and bounded tree-width, every property that is expressible in monadic second-order logic with counting (CMSO) is testable with constant query complexity and <i>sublinear</i> running time. It remains open whether this can be improved to constant running time.</p><p>In this article we introduce a new model, which is based on the bounded degree model, but the distance measure allows both edge (tuple) modifications and vertex (element) modifications. We show that every property that is testable in the classical model is testable in our model with the same query complexity and running time, but the converse is not true. Our main theorem shows that on databases of bounded degree and bounded tree-width, every property that is expressible in CMSO is testable with constant query complexity and <i>constant</i> running time in the new model. Our proof methods include the semilinearity of the neighborhood histograms of databases having the property and a result by Alon (Proposition 19.10 in Lovász, Large networks and graph limits, 2012) that states that for every bounded degree graph (mathcal {G}) there exists a constant size graph (mathcal {H}) that has a similar neighborhood distribution to (mathcal {G}).</p><p>It can be derived from a result in (Benjamini et al., Advances in Mathematics 2010) that hyperfinite hereditary properties are testable with constant query complexity and constant running time in the classical model (and hence in the new model). Using our methods, we give an alternative proof that hyperfinite hereditary properties are testable with constant query complexity and constant running time in the new model.</p><p>We argue that our model is natural and our meta-theorem showing constant-time CMSO testability supports this.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"38 7","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameterized Complexity of Logic-based Argumentation in Schaefer’s Framework","authors":"Yasir Mahmood, Arne Meier, Johannes Schmidt","doi":"https://dl.acm.org/doi/10.1145/3582499","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3582499","url":null,"abstract":"<p>Argumentation is a well-established formalism dealing with conflicting information by generating and comparing arguments. It has been playing a major role in AI for decades. In logic-based argumentation, we explore the internal structure of an argument. Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this article, we study the propositional variants of the following three computational tasks studied in argumentation: ARG (exists a support for a given claim with respect to a given set of formulas), ARG-Check (is a given set a support for a given claim), and ARG-Rel (similarly as ARG plus requiring an additionally given formula to be contained in the support). ARG-Check is complete for the complexity class DP, and the other two problems are known to be complete for the second level of the polynomial hierarchy (Creignou et al. 2014 and Parson et al., 2003) and, accordingly, are highly intractable. Analyzing the reason for this intractability, we perform a two-dimensional classification: First, we consider all possible propositional fragments of the problem within Schaefer’s framework (STOC 1978) and then study different parameterizations for each of the fragments. We identify a list of reasonable structural parameters (size of the claim, support, knowledge base) that are connected to the aforementioned decision problems. Eventually, we thoroughly draw a fine border of parameterized intractability for each of the problems showing where the problems are fixed-parameter tractable and when this exactly stops. Surprisingly, several cases are of very high intractability (para-NP and beyond).</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"38 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixed Iterated Revisions: Rationale, Algorithms, and Complexity","authors":"Paolo Liberatore","doi":"https://dl.acm.org/doi/10.1145/3583071","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3583071","url":null,"abstract":"<p>Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refinement, and severe withdrawal. In turn, these three can be expressed in terms of lexicographic revision at the cost of restructuring the sequence. This restructuring needs not to be done explicitly: an algorithm that works on the original sequence is shown. The complexity of mixed sequences of belief change operators is also analyzed. Most of them require only a polynomial number of calls to a satisfiability checker, some are even easier.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"39 7","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Decidable Fragment of First Order Modal Logic: Two Variable Term Modal Logic","authors":"A. Padmanabha, R. Ramanujam","doi":"10.1145/3593584","DOIUrl":"https://doi.org/10.1145/3593584","url":null,"abstract":"First order modal logic (𝖥𝖮𝖬𝖫) is built by extending First Order Logic (𝖥𝖮) with modal operators. A typical formula is of the form (forall x exists y Box P(x,y)) . Not only is 𝖥𝖮𝖬𝖫 undecidable, even simple fragments like that of restriction to unary predicate symbols, guarded fragment and two variable fragment, which are all decidable for 𝖥𝖮 become undecidable for 𝖥𝖮𝖬𝖫. In this paper we study Term Modal logic (𝖳𝖬𝖫) which allows modal operators to be indexed by terms. A typical formula is of the form (forall x exists y~Box _x P(x,y)) . There is a close correspondence between 𝖳𝖬𝖫 and 𝖥𝖮𝖬𝖫 and we explore this relationship in detail in the paper. In contrast to 𝖥𝖮𝖬𝖫, we show that the two variable fragment (without constants, equality) of 𝖳𝖬𝖫 is decidable. Further, we prove that adding a single constant makes the two variable fragment of 𝖳𝖬𝖫 undecidable. On the other hand, when equality is added to the logic, it loses the finite model property.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":" ","pages":"1 - 38"},"PeriodicalIF":0.5,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48757506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interval Temporal Logic for Visibly Pushdown Systems","authors":"Laura Bozzelli, Angelo Montanari, Adriano Peron","doi":"https://dl.acm.org/doi/10.1145/3583756","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3583756","url":null,"abstract":"<p>In this article, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic <sans-serif>HS</sans-serif> for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures enforcing visibility of the pushdown operations. The proposed logic, called nested <sans-serif>BHS</sans-serif>, supports branching-time both in the past and in the future and is able to express non-regular properties of linear and branching behaviours of procedural contexts in a natural way. It strictly subsumes well-known linear time context-free extensions of <sans-serif>LTL</sans-serif> such as <sans-serif>CaRet</sans-serif> [4] and <sans-serif>NWTL</sans-serif> [2]. The main result is the decidability of the visibly pushdown model-checking problem against nested <sans-serif>BHS</sans-serif>. The proof exploits a non-trivial automata-theoretic construction.</p><p></p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"36 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}