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  • α β-Relations and the Actual Meaning of α-Renaming
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2021-01-15
    Michele Basaldella

    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

  • Strategy Logic with Imperfect Information
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2021-01-05
    Raphaël Berthon; Bastien Maubert; Aniello Murano; Sasha Rubin; Moshe Y. Vardi

    We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, this problem is undecidable; but we introduce a syntactical class of “hierarchical instances” for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications

  • Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2021-01-05
    Bart Bogaerts; Luís Cruz-Filipe

    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

  • Alternating Tree Automata with Qualitative Semantics
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-12-17
    Raphaël Berthon; Nathanaël Fijalkow; Emmanuel Filiot; Shibashis Guha; Bastien Maubert; Aniello Murano; Laureline Pinault; Sophie Pinchinat; Sasha Rubin; Olivier Serre

    We study alternating automata with qualitative semantics over infinite binary trees: Alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this article, we prove a positive and a negative result for the emptiness problem of alternating

  • Beyond Uniform Equivalence between Answer-set Programs
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-12-02
    Johannes Oetsch; Martina Seidl; Hans Tompits; Stefan Woltran

    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

  • Principles of KLM-style Defeasible Description Logics
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-11-15
    Katarina Britz; Giovanni Casini; Thomas Meyer; Kody Moodley; Uli Sattler; Ivan Varzinczak

    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

  • Model Checking a Logic for True Concurrency
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-10-26
    Paolo Baldan; Tommaso Padoan

    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

  • Applying Visible Strong Equivalence in Answer-Set Program Transformations
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-10-17
    Jori Bomanson; Tomi Janhunen; Ilkka Niemelä

    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

  • Undecidable Cases of Model Checking Probabilistic Temporal-Epistemic Logic
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-10-13
    Ron Van Der Meyden; Manas K. Patra

    We investigate the decidability of model checking logics of time, knowledge, and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observable discrete-time Markov chains. Decidability results are known for certain restricted logics with respect to these semantics, subject to a variety of restrictions that are either unexplained or

  • Finite Open-world Query Answering with Number Restrictions
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-07-05
    Antoine Amarilli; Michael Benedikt

    Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions

  • A New Perspective on FO Model Checking of Dense Graph Classes
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-07-05
    Jakub Gajarský; Petr Hliněný; Jan Obdržálek; Daniel Lokshtanov; M. S. Ramanujan

    We study the first-order (FO) model checking problem of dense graph classes, namely, those that have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes that are FO interpretable in graphs of bounded degree. This characterization allows us to efficiently compute such an FO interpretation for an input graph. As a consequence

  • First-Order Interpretations of Bounded Expansion Classes
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-07-05
    Jakub Gajarský; Stephan Kreutzer; Jaroslav NešETřil; Patrice Ossona De Mendez; Michał Pilipczuk; Sebastian Siebertz; Szymon Toruńczyk

    The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined

  • Metric Temporal Description Logics with Interval-Rigid Names
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-08-11
    Franz Baader; Stefan Borgwardt; Patrick Koopmann; Ana Ozaki; Veronika Thost

    In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining description logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there is a growing interest in

  • Non-well-founded Proof Theory of Transitive Closure Logic
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-08-11
    Liron Cohen; Reuben N. S. Rowe

    Supporting inductive reasoning is an essential component is any framework of use in computer science. To do so, the logical framework must extend that of first-order logic. Transitive closure logic is a known extension of first-order logic that is particularly straightforward to automate. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive

  • Inputs and Outputs in CSP
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-05-11
    Ana Cavalcanti; Robert M. Hierons; Sidney Nogueira

    This article addresses refinement and testing based on CSP models, when we distinguish input and output events. In a testing experiment, the tester (or the environment) controls the inputs, and the system under test controls the outputs. The standard models and refinement relations of CSP, however, do not differentiate inputs and outputs and are not, therefore, entirely suitable for testing. Here,

  • Typal Heterogeneous Equality Types
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-04-19
    Andrew M. Pitts

    The usual homogeneous form of equality type in Martin-Löf Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly different types. This short note introduces a simple set of axioms for such types. The axioms are shown to be equivalent to the combination of systematic elimination rules

  • Model Checking MITL Formulae on Timed Automata
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-04-10
    Claudio Menghi; Marcello M. Bersani; Matteo Rossi; Pierluigi San Pietro

    Timed Automata (TA) is de facto a standard modelling formalism to represent systems when the interest is the analysis of their behaviour as time progresses. This modelling formalism is mostly used for checking whether the behaviours of a system satisfy a set of properties of interest. Even if efficient model-checkers for Timed Automata exist, these tools are not easily configurable. First, they are

  • Toward a Uniform Theory of Effectful State Machines
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-03-13
    Sergey Goncharov; Stefan Milius; Alexandra Silva

    Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g., finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs’s notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual

  • Why Liveness for Timed Automata Is Hard, and What We Can Do About It
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-03-03
    Frédéric Herbreteau; B. Srivathsan; Thanh-Tung Tran; Igor Walukiewicz

    The reachability problem for timed automata asks if a given automaton has a run leading to an accepting state, and the liveness problem asks if the automaton has an infinite run that visits accepting states infinitely often. Both of these problems are known to be Pspace-complete.

  • Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-03-03
    Camillo Fiorentini; Mauro Ferrari

    The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate

  • The Bernays-Schönfinkel-Ramsey Class of Separation Logic with Uninterpreted Predicates
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-02-25
    Mnacho Echenim; Radu Iosif; Nicolas Peltier

    This article investigates the satisfiability problem for Separation Logic with k record fields, with unrestricted nesting of separating conjunctions and implications. It focuses on prenex formulæ with a quantifier prefix in the language ∃*∀* that contain uninterpreted (heap-independent) predicate symbols. In analogy with first-order logic, we call this fragment Bernays-Schönfinkel-Ramsey Separation

  • Linking Focusing and Resolution with Selection
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-02-20
    Guillaume Burel

    Focusing and selection are techniques that shrink the proof-search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atomic formula can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove

  • Dichotomies in Ontology-Mediated Querying with the Guarded Fragment
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-02-20
    André Hernich; Carsten Lutz; Fabio Papacchini; Frank Wolter

    We study ontology-mediated querying in the case where ontologies are formulated in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries. Our aim is to classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O, where query evaluation w.r.t. O is in PTime (resp.

  • How Good Is a Strategy in a Game with Nature?
    ACM Trans. Comput. Log. (IF 0.688) Pub Date : 2020-02-20
    Arnaud Carayol; Olivier Serre

    We consider games with two antagonistic players—Éloïse (modelling a program) and Abélard (modelling a Byzantine environment)—and a third, unpredictable and uncontrollable player, which we call Nature. Motivated by the fact that the usual probabilistic semantics very quickly leads to undecidability when considering either infinite game graphs or imperfect-information, we propose two alternative semantics

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