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An Axiomatic Theory for Reversible Computation ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240219
Ivan Lanese, Iain Phillips, Irek UlidowskiUndoing computations of a concurrent system is beneficial in many situations, e.g., in reversible debugging of multithreaded programs and in recovery from errors due to optimistic execution in parallel discrete event simulation. A number of approaches have been proposed for how to reverse formal models of concurrent computation including process calculi such as CCS, languages like Erlang, and abstract

Spectrum of FO Logic With Quantifier Depth 4 Is Finite ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240122
Yury Yarovikov, Maksim ZhukovskiiThe kspectrum is the set of all α > 0 such that G(n, n− α) does not obey the 01 law for FO sentences with quantifier depth at most k. In this paper, we prove that the minimum k such that the kspectrum is infinite equals 5.

Perspective Games ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240117
Orna Kupferman, Gal VardiWe introduce and study perspective games, which model multiagent systems in which agents can view only the parts of the system that they own. As in standard multiplayer turnbased games, the vertices of the game graph are partitioned among the players. Starting from an initial vertex, the players jointly generate a computation, with each player deciding the successor vertex whenever the generated

Products, Polynomials and Differential Equations in the Stream Calculus ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240117
Michele Boreale, Luisa Collodi, Daniele GorlaWe study connections among polynomials, differential equations, and streams over a field 𝕂, in terms of algebra and coalgebra. We first introduce the class of (F,G)products on streams, those where the stream derivative of a product can be expressed as a polynomial function of the streams and their derivatives. Our first result is that, for every (F,G)product, there is a canonical way to construct

Algebraic Proof Theory for LElogics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240117
Giuseppe Greco, Peter Jipsen, Fei Liang, Alessandra Palmigiano, Apostolos TzimoulisIn this article, we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LElogics). Specifically, we generalize the residuated frames in Reference [34] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable

Decidability of the Satisfiability Problem for Boolean Set Theory with the Unordered Cartesian Product Operator ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240116
Domenico Cantone, Pietro UrsinoWe give a positive solution to the decidability problem for the fragment of set theory, dubbed BST⊗, consisting of quantifierfree formulae involving the Boolean set operators of union, intersection, and set difference, along with the unordered Cartesian product operator ⊗ (where \(s \otimes t := \big \lbrace \lbrace u,v\rbrace \,\texttt {}\:u \in s \wedge v \in t \big \rbrace\)), and the equality

On the Complexity of Model Checking Knowledge and Time ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20240116
Laura Bozzelli, Bastien Maubert, Aniello MuranoWe establish the precise complexity of the modelchecking problem for the main logics of knowledge and time. While this problem was known to be nonelementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for 20 years. We close

Comparing the Expressiveness of the πcalculus and CCS ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20231118
Rob van GlabbeekThis paper shows that the πcalculus with implicit matching is no more expressive than CCSγ, a variant of CCS in which the result of a synchronisation of two actions is itself an action subject to relabelling or restriction, rather than the silent action τ. This is done by exhibiting a compositional translation from the πcalculus with implicit matching to CCSγ that is valid up to strong barbed bisimilarity

Extensible Proof Systems for InfiniteState Systems ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20231118
Rance Cleaveland, Jeroen J. A. KeirenThis article revisits soundness and completeness of proof systems for proving that sets of states in infinitestate labeled transition systems satisfy formulas in the modal mucalculus in order to develop proof techniques that permit the seamless inclusion of new features in this logic. Our approach relies on novel results in lattice theory, which give constructive characterizations of both greatest

A Decision Procedure for a Theory of Finite Sets with Finite Integer Intervals ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20231118
Maximiliano Cristiá, Gianfranco RossiIn this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints (ℒ⋅) to a decision procedure for ℒ⋅ extended with set terms denoting finite integer intervals (ℒ[]). In ℒ[] interval limits can be integer linear terms including unbounded variables. These intervals are a useful extension because they allow to express nontrivial set operators such as

Living without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20231010
Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank WolterThe 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

Inputs, Outputs, and Composition in the Logic of Information Flows ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230825
Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den BusscheThe logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logicbased fashion. The first contribution of this article 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

Firstorder Logic with Connectivity Operators ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230725
Nicole Schirrmacher, Sebastian Siebertz, Alexandre VignyFirstorder logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem parameterized by solution size. However, FO cannot express the very simple algorithmic question whether two vertices are connected. We enrich FO with connectivity predicates that are tailored to express algorithmic graph problems that are commonly studied in parameterized algorithmics

Generating Extended Resolution Proofs with a BDDBased SAT Solver ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230725
Randal E. Bryant, Marijn J. H. HeuleIn 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical framework. Through this, a BDDbased Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability. Such a proof indicates that the formula

Local Search For Satisfiability Modulo Integer Arithmetic Theories ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230725
Shaowei Cai, Bohan Li, Xindi ZhangSatisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background firstorder theories. In this article, we focus on Satisfiablity Modulo Integer Arithmetic, which is referred to as SMT(IA), including both linear and nonlinear integer arithmetic theories. Dominant approaches to SMT rely on calling a CDCLbased SAT solver, either

Inputs, Outputs, and Composition in the Logic of Information Flows ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230715
Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den BusscheThe logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logicbased 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

Interpolation Results for Arrays with Length and MaxDiff ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230609
Silvio Ghilardi, Alessandro Gianola, Deepak Kapur, Chiara NasoIn this article, we enrich McCarthy’s theory of extensional arrays with a length and a maxdiff operation. As is wellknown, 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

A Decidable Fragment of First Order Modal Logic: Two Variable Term Modal Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230609
Anantha Padmanabha, R. RamanujamFirst 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

Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230603
Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank WolterThe 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

Faster Property Testers in a Variation of the Bounded Degree Model ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230510
Isolde Adler, Polly FaheyProperty testing algorithms are highly efficient algorithms that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the distance is measured by the number of edge modifications (additions

Parameterized Complexity of Logicbased Argumentation in Schaefer’s Framework ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230510
Yasir Mahmood, Arne Meier, Johannes SchmidtArgumentation is a wellestablished formalism dealing with conflicting information by generating and comparing arguments. It has been playing a major role in AI for decades. In logicbased 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, subsetminimal, and implies the claim. In such a case, the pair

Mixed Iterated Revisions: Rationale, Algorithms, and Complexity ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230510
Paolo LiberatoreSeveral 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

Interval Temporal Logic for Visibly Pushdown Systems ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230417
Laura Bozzelli, Angelo Montanari, Adriano PeronIn this article, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic HS for the specification and verification of branchingtime contextfree requirements of pushdown systems under a statebased semantics over Kripke structures enforcing visibility of the pushdown operations. The proposed logic, called nested BHS, supports branchingtime both in the past and in

Circular (Yet Sound) Proofs in Propositional Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230407
Albert Atserias, Massimo LauriaProofs in propositional logic are typically presented as trees of derived formulas or, alternatively, as directed acyclic graphs of derived formulas. This distinction between treelike vs. daglike structure is particularly relevant when making quantitative considerations regarding, for example, proof size. Here we analyze a more general type of structural restriction for proofs in rulebased proof

Reasoning about Quality and Fuzziness of Strategic Behaviors ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230407
Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, Giuseppe PerelliTemporal logics are extensively used for the specification of ongoing behaviors of computer systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of ongoing strategic behaviors in multiagent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable

Eager Equality for Rational Number Arithmetic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230407
Jan A. Bergstra, John V. TuckerEager equality for algebraic expressions over partial algebras distinguishes or separates terms only if both have defined values and they are different. We consider arithmetical algebras with division as a partial operator, called meadows, and focus on algebras of rational numbers. To study eager equality, we use common meadows, which are totalisations of partial meadows by means of absorptive elements

Number of Variables for Graph Differentiation and the Resolution of Graph Isomorphism Formulas ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230407
Jacobo Torán, Florian WörzWe show that the number of variables and the quantifier depth needed to distinguish a pair of graphs by firstorder logic sentences exactly match the complexity measures of clause width and depth needed to refute the corresponding graph isomorphism formula in propositional narrow resolution. Using this connection, we obtain upper and lower bounds for refuting graph isomorphism formulas in (normal)

Semantic Analysis of a Linear Temporal Extension of Quantum Logic and Its Dynamic Aspect ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230317
Tsubasa TakagiAlthough various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints have not been studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear temporal extension of quantum logic with a quantum implication, and extend it to Dynamic Linear Temporal Quantum Logic (DLTQL). This logic has temporal operators to express

Hardness Characterisations and Sizewidth Lower Bounds for QBF Resolution ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230127
Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan, Tomáš PeitlWe provide a tight characterisation of proof size in resolution for quantified Boolean formulas (QBF) via circuit complexity. Such a characterisation was previously obtained for a hierarchy of QBF Frege systems [16], but leaving open the most important case of QBF resolution. Different from the Frege case, our characterisation uses a new version of decision lists as its circuit model, which is stronger

Linear Logic Properly Displayed ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230128
Giuseppe Greco, Alessandra PalmigianoWe introduce proper display calculi for intuitionistic, biintuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut elimination and subformula property. Based on the same design, we introduce a variant of Lambek calculus with exponentials, aimed at capturing the controlled application of exchange and associativity. Properness (i.e., closure

Testing using CSP Models: Time, Inputs, and Outputs ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230128
James Baxter, Ana Cavalcanti, Maciej Gazda, Robert M. HieronsThe existing testing theories for CSP cater for verification of interaction patterns (traces) and deadlocks, but not time. We address here refinement and testing based on a dialect of CSP, called tockCSP, which can capture discrete time properties. This version of CSP has been of widespread interest for decades; recently, it has been given a denotational semantics, and model checking has become possible

Witnesses for Answer Sets of Logic Programs ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230127
Yisong Wang, Thomas Eiter, Yuanlin Zhang, Fangzhen LinIn this article, we consider Answer Set Programming (ASP). It is a declarative problem solving paradigm that can be used to encode a problem as a logic program whose answer sets correspond to the solutions of the problem. It has been widely applied in various domains in AI and beyond. Given that answer sets are supposed to yield solutions to the original problem, the question of “why a set of atoms

Generalizing Parikh’s Criterion for RelevanceSensitive Belief Revision ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230127
Theofanis AravanisParikh proposed his relevancesensitive axiom to remedy the weakness of the classical AGM paradigm in addressing relevant change. An insufficiency of Parikh’s criterion, however, is its dependency on the contingent beliefs of a belief set to be revised, since the former only constrains the revision process of splittable theories (i.e., theories that can be divided in mutually disjoint compartments)

GoodforGame QPTL: An Alternating Hodges Semantics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230123
Dylan Bellier, Massimo Benerecetti, Dario Della Monica, Fabio MogaveroAn extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in gametheory and allows the resulting logic to naturally express gametheoretic concepts. Inspired by the work

Logics for Temporal Information Systems in Rough Set Theory ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230120
Md. Aquil Khan, Mohua Banerjee, Sibsankar PandaThe article discusses temporal information systems (TISs) that add the dimension of time to complete or incomplete information systems. Through TISs, one can accommodate the possibility of domains or attribute values for objects changing with time or the availability of currently missing information with time. Different patterns of flow of information give different TISs. The corresponding logics with

A Decision Procedure for Guarded Separation Logic Complete Entailment Checking for Separation Logic with Inductive Definitions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Christoph Matheja, Jens Pagel, Florian ZulegerWe develop a doubly exponential decision procedure for the satisfiability problem of guarded separation logic—a novel fragment of separation logic featuring usersupplied inductive predicates, Boolean connectives, and separating connectives, including restricted (guarded) versions of negation, magic wand, and septraction. Moreover, we show that dropping the guards for any of the preceding connectives

Continuous Onecounter Automata ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Michael Blondin, Tim Leys, Filip Mazowiecki, Philip Offtermatt, Guillermo PérezWe study the reachability problem for continuous onecounter automata, COCA for short. In such automata, transitions are guarded by upper and lowerbound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (nondeterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: we prove (1) that the

The Complexity of Quantified Constraints: Collapsibility, Switchability, and the Algebraic Formulation ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Catarina Carvalho, Florent Madelaine, Barnaby Martin, Dmitriy ZhukLet 𝔸 be an idempotent algebra on a finite domain. By mediating between results of Chen [1] and Zhuk [2], we argue that if 𝔸 satisfies the polynomially generated powers property (PGP) and ℬ is a constraint language invariant under 𝔸 (i.e., in Inv(𝔸)), then QCSP ℬ is in NP. In doing this, we study the special forms of PGP, switchability, and collapsibility, in detail, both algebraically and logically

Canonisation and Definability for Graphs of Bounded Rank Width ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Martin Grohe, Daniel NeuenWe prove that the combinatorial WeisfeilerLeman algorithm of dimension (3k+4) is a complete isomorphism test for the class of all graphs of rank width at most k. Rank width is a graph invariant that, similarly to tree width, measures the width of a certain style of hierarchical decomposition of graphs; it is equivalent to clique width. It was known that isomorphism of graphs of rank width k is decidable

SATInspired Eliminations for Superposition ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Petar Vukmirović, Jasmin Blanchette, Marijn J. H. HeuleOptimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to firstorder logic with equality. In this article, we port inprocessing techniques to work with superposition, a leading firstorder proof calculus, and we strengthen known preprocessing techniques. Specifically, we look into elimination

MaxSAT Resolution and Subcube Sums ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Yuval Filmus, Meena Mahajan, Gaurav Sood, Marc VinyalsWe study the MaxSAT Resolution (MaxRes) rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than treelike resolution, and when augmented with weakening (the system MaxResW), psimulates treelike resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new proof system called

Reducible Theories and Amalgamations of Models ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230118
Bahar Aameri, Michael GrüningerWithin knowledge representation in artificial intelligence, a firstorder ontology is a theory in firstorder logic that axiomatizes the concepts in some domain. Ontology verification is concerned with the relationship between the intended models of an ontology and the models of the axiomatization of the ontology. In particular, we want to characterize the models of an ontology up to isomorphism and

On monotonic determinacy and rewritability for recursive queries and views ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20230105
Michael Benedikt, Stanislav Kikot, Piotr OstropolskiNalewaja, Miguel RomeroA query Q is monotonically determined over a set of views V if Q can be expressed as a monotonic function of the view image. In the case of relational algebra views and queries, monotonic determinacy coincides with rewritability as a union of conjunctive queries, and it is decidable in important special cases, such as for CQ views and queries [11, 30]. We investigate the situation for views and queries

On Composing Finite Forests with Modal Logics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221229
Bartosz Bednarczyk, Stéphane Demri, Raul Fervari, Alessio MansuttiWe study the expressivity and complexity of two modal logics interpreted on finite forests and equipped with standard modalities to reason on submodels. The logic \(\mathsf {ML} (\,\operatorname{\raisebox {2pt}{\rule {1.2pt}{2.1ex}}}\,) \) extends the modal logic K with the composition operator \(\operatorname{\raisebox {2pt}{\rule {1.2pt}{2.1ex}}} \) from ambient logic, whereas \(\mathsf {ML} (\mathbin

GoodforGame QPTL: An Alternating Hodges Semantics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221021
Dylan Bellier, Massimo Benerecetti, Dario Della Monica, Fabio MogaveroAn extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in gametheory and allows the resulting logic to naturally express gametheoretic concepts. Inspired by the work

Precise Subtyping for Asynchronous Multiparty Sessions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Silvia Ghilezan, Jovanka Pantović, Ivan Prokić, Alceste Scalas, Nobuko YoshidaSession subtyping is a cornerstone of refinement of communicating processes: a process implementing a session type (i.e., a communication protocol) T can be safely used whenever a process implementing one of its supertypes T′ is expected, in any context, without introducing deadlocks nor other communication errors. As a consequence, whenever T ≤ T′ holds, it is safe to replace an implementation of

The Temporal Logic of Coalitional Goal Assignments in Concurrent Multiplayer Games ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Sebastian Enqvist, Valentin GorankoWe introduce and study a natural extension of the Alternating time temporal logic ATL, called Temporal Logic of Coalitional Goal Assignments (TLCGA). It features one new and quite expressive coalitional strategic operator, called the coalitional goal assignment operator ⦉ γ ⦊, where γ is a mapping assigning to each set of players in the game its coalitional goal, formalised by a path formula of the

Are Two Binary Operators Necessary to Obtain a Finite Axiomatisation of Parallel Composition? ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Ingólfsdóttir, Bas LuttikBergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy’s merge is added to that language. These results raise the question

Syntactic Completeness of Proper Display Calculi ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Jinsheng Chen, Giuseppe Greco, Alessandra Palmigiano, Apostolos TzimoulisA recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e., those calculi that support general and modular proofstrategies for cut elimination) and at identifying classes of logics that can be captured in terms of these calculi. In this context, Wansing introduced the notion of proper display calculi as one possible design framework for proof calculi

The Intersection of Algorithmically Random Closed Sets and Effective Dimension ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Adam Case, Christopher P. PorterIn this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (random with respect to certain underlying measures induced by Bernoulli measures on the space of codes of closed sets), which preserves randomness, can be inverted: a random closed

A Category Theoretic View of Contextual Types: From Simple Types to Dependent Types ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Jason Z. S. Hu, Brigitte Pientka, Ulrich SchöppWe describe the categorical semantics for a simply typed variant and a simplified dependently typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higherorder abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard

A Subatomic Proof System for Decision Trees ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Chris Barrett, Alessio GuglielmiWe design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunctiondisjunctionnegation and binary decision trees. We give two reasons to do so. The first is prooftheoretical naturalness: The system consists of all and only the inference rules generated by the single, simple, linear scheme of the recently introduced subatomic logic

Unifying Operational Weak Memory Verification: An Axiomatic Approach ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20221020
Simon Doherty, Sadegh Dalvandi, Brijesh Dongol, Heike WehrheimIn this article, we propose an approach to program verification using an abstract characterisation of weak memory models. Our approach is based on a hierarchical axiom scheme that captures the observational properties of a memory model. In particular, we show that it is possible to prove correctness of a program with respect to a particular axiom scheme, and we show this proof to suffice for any memory

A Generalized Realizability and Intuitionistic Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220929
Aleksandr Yu. KonovalovLet V be a set of numbertheoretical functions. We define a notion of Vrealizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this paper we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of Vrealizability if and only if some natural conditions for V hold.

On Proof Complexity of Resolution over Polynomial Calculus ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220722
Erfan KhanikiThe proof system Res (PCd,R) is a natural extension of the Resolution proof system that instead of disjunctions of literals operates with disjunctions of degree d multivariate polynomials over a ring R with Boolean variables. Proving superpolynomial lower bounds for the size of Res(PC1,R)refutations of Conjunctive normal forms (CNFs) is one of the important problems in propositional proof complexity

Logics for Temporal Information Systems in Rough Set Theory ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220719
MD. Aquil Khan, Mohua Banerjee, Sibsankar PandaThe article discusses temporal information systems (TISs) that add the dimension of time to complete or incomplete information systems. Through TISs, one can accommodate the possibility of domains or attributevalues for objects changing with time or the availability of currently missing information with time. Different patterns of flow of information give different temporal information systems. The

A Category Theoretic View of Contextual Types: from Simple Types to Dependent Types ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220629
Jason Z. S. Hu, Brigitte Pientka, Ulrich SchöppWe describe the categorical semantics for a simply typed variant and a simplified dependently typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higherorder abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard

A Subatomic Proof System for Decision Trees ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220628
Chris Barrett, Alessio GuglielmiWe design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunctiondisjunctionnegation and binary decision trees. We give two reasons to do so. The first is prooftheoretical naturalness: the system consists of all and only the inference rules generated by the single, simple, linear scheme of the recently introduced subatomic logic

Unifying Operational Weak Memory Verification: An Axiomatic Approach ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220627
Simon Doherty, Sadegh Dalvandi, Brijesh Dongol, Heike WehrheimIn this paper, we propose an approach to program verification using an abstract characterisation of weak memory models. Our approach is based on a hierarchical axiom scheme that captures the observational properties of a memory model. In particular, we show that it is possible to prove correctness of a program with respect to a particular axiom scheme, and show this proof to suffice for any memory

The Intersection of Algorithmically Random Closed Sets and Effective Dimension ACM Trans. Comput. Log. (IF 0.5) Pub Date : 20220625
Adam Case, Christopher P. PorterIn this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to certain underlying measures induced by Bernoulli measures on the space of codes of closed sets), which preserves randomness, can be inverted: a random closed set