ACM Transactions on

Computational Logic (TOCL)

Latest Articles

Central Limit Model Checking

We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from exponential... (more)

A Representation Theorem for Change through Composition of Activities

The expanding use of information systems in industrial and commercial settings has increased the need for interoperation between software systems. In... (more)

Reasoning about Cognitive Trust in Stochastic Multiagent Systems

We consider the setting of stochastic multiagent systems modelled as stochastic multiplayer games and formulate an automated verification framework... (more)

De Morgan Dual Nominal Quantifiers Modelling Private Names in Non-Commutative Logic

This article explores the proof theory necessary for recommending an expressive but decidable first-order system, named MAV1, featuring a De Morgan... (more)

Modal Resolution: Proofs, Layers, and Refinements

Resolution-based provers for multimodal normal logics require pruning of the search space for a proof to ameliorate the inherent intractability of the satisfiability problem for such logics. We present a clausal modal-layered hyper-resolution calculus for the basic multimodal logic, which divides the clause set according to the modal level at which... (more)

Incomplete SMT Techniques for Solving Non-Linear Formulas over the Integers

We present new methods for solving the Satisfiability Modulo Theories problem over the theory of Quantifier-Free Non-linear Integer Arithmetic,... (more)


TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. The journal is published quarterly. The first issue appeared in July 2000, and the journal is indexed by ISI beginning with the 2006 volume. About

Forthcoming Articles

Monadic Datalog, Tree Validity, and Limited Access Containment

We reconsider the problem of containment of monadic datalog (MDL) queries in unions of conjunctive queries (UCQs). Prior work has dealt with special cases of the problem, but has left the precise complexity characterization open. In addition, the complexity of one important special case, that of containment under access patterns, was not known before. We start by revisiting the connection between MDL/UCQ containment and containment problems involving regular tree languages. We then present a general approach for getting tighter bounds on the complexity of query containment, based on analysis of the number of mappings of queries into tree-like instances. We give two applications of the machinery. We first give an important special case of the MDL/UCQ containment problem that is in EXPTIME, and use this bound to show an $\exptime$ bound on containment under access patterns. Secondly we show that the same technique can be used to get a new tight upper bound for containment of tree automata in UCQs. We finally show that the new MDL/UCQ upper bounds are tight. We establish a 2EXPTIME lower bound on the MDL/UCQ containment problem, resolving an open problem from the early 1990s. We also show that changes to the conditions given in our special cases can not be eliminated, and that in particular slight variations of the problem of containment under access patterns become TWOEXPTIME-complete.

Verification Methods for the Computationally Complete Symbolic Attacker Based on Indistinguishability

In recent years, a new approach has been developed for verifying security protocols with the aim of combining the benefits of symbolic attackers and the benefits of unconditional soundness: the technique of the computationally complete symbolic attacker of Bana and Comon (BC). In this paper we argue that the real breakthrough of this technique is the recent introduction of its version for indistinguishability because, with the extensions we introduce here, for the first time, there is a computationally sound symbolic technique that is syntactically strikingly simple, to which translating standard computational security notions is a straightforward matter, and that can be effectively used for verification of not only equivalence properties, but trace properties of protocols as well. We first fully develop the core elements of this newer version by introducing several new axioms. We illustrate the power and the diverse use of the introduced axioms on simple examples first. We introduce an axiom expressing the Decisional Diffie-Hellman property. We analyze the Diffie-Hellman key exchange, both in its simplest form and an authenticated version as well. We provide computationally sound verification of real-or-random secrecy of the Diffie-Hellman key exchange protocol for multiple sessions, without any restrictions on the computational implementation other than the DDH assumption. We also show authentication for a simplified version of the station-to-station protocol using UF-CMA assumption for digital signatures. Finally, we axiomatize IND-CPA, IND-CCA1 and IND-CCA2 security properties and illustrate their usage. We have formalized the axiomatic system in an interactive theorem prover, Coq, and have machine- checked the proofs of various auxiliary theorems, and security properties of Diffie-Hellman and station-to-station protocol.

Adding successor: A transfer theorem for separation and covering

Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the second. Separation is usually investigated as a means to obtain a deep understanding of the class C. In the paper, we are mainly interested in classes defined by logical formalisms. Such classes are often built on top of each other: given some logic, one builds a stronger one by adding new predicates to its signature. A natural construction is to enrich a logic with the successor relation. In this paper, we present a transfer result applying to this construction: we show that for suitable logically defined classes, separation for the logic enriched with the successor relation reduces to separation for the original logic. Our theorem also applies to a problem that is stronger than separation: covering. Moreover, we actually present two reductions: one for languages of finite words and the other for languages of infinite words.

Dynamic QBF Dependencies in Reduction and Expansion

We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of inprocessing. Formalising this notion, we introduce a new version of Q-resolution in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation. Lastly, we show that the same picture emerges in an analogous approach to the universal expansion paradigm.

Typing messages for free in security protocols

Security properties of cryptographic protocols are typically expressed as reachability or equivalence properties. Secrecy and authentication are examples of reachability properties while privacy properties such as untraceability, vote secrecy, or anonymity are generally expressed as behavioural equivalence in a process algebra that models security protocols. Our main contribution is to reduce the search space for attacks for reachability as well as equivalence properties. Specifically, we show that if there is an attack then there is one that is well-typed. Our result holds for a large class of typing systems, a family of equational theories that encompasses all standard primitives, and a large class of deterministic security protocols. For many standard protocols, we deduce that it is sufficient to look for attacks that follow the format of the messages expected in an honest execution, therefore considerably reducing the search space.

Runtime Verification over Out-of-order Streams

We present an approach for verifying systems at runtime. Our approach targets distributed systems whose components communicate with monitors over unreliable channels, where messages can be delayed, reordered, or even lost. Furthermore, our approach handles an expressive specifications language that extends the real-time logic MTL with freeze quantifiers for reasoning about data values. The logic's main novelty is a new three-valued semantics that is well suited for runtime verification as it accounts for partial knowledge about system behavior. Based on this semantics, we present online algorithms that reason soundly and completely about streams where events can occur out of order. We also evaluate our algorithms experimentally. Depending on the specification, our prototype implementation scales to out-of-order streams with hundreds to thousands of events per second.

Reason-maintenance Belief Logic with Uncertain Information

In this paper, we propose a logic for reasoning about belief based on fusion of uncertain information. The resultant reason-maintenance possibilistic belief logic can represent both implicit and explicit uncertain beliefs of an agent. While implicit beliefs stipulate what are believable, explicit beliefs can trace the process of belief formation by information fusion. To set up the basic framework, we start with developing a reason-maintenance belief logic without uncertainty, present its syntax and semantics, and investigate its axiomatization and properties. We also demonstrate its applicability by using a realistic example in system accountability. Then, we extend the basic logic to accommodate the possibilistic uncertainty of information and belief, provide a complete axiomatization of the extended logic, and show that it can address the reason-maintenance issue of partially inconsistent belief.

Satisfiability of Modal Inclusion Logic: Lax and Strict Semantics

We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be EXPTIME-complete on general structures. Finally, we show how for a specific class of structures NEXPTIME-completeness for these problems under strict semantics can be achieved.

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