Efficient First-Order Temporal Logic for Infinite-State Systems

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.Comment: 16 pages, 2 figure

Undecidability of first-order modal and intuitionistic logics with two variables and one monadic predicate letter

We prove that the positive fragment of first-order intuitionistic logic in the language with two variables and a single monadic predicate letter, without constants and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals [QBL, QKC] and [QBL, QFL], where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser's basic and formal logics, respectively. We also show that, for most "natural" first-order modal logics, the two-variable fragment with a single monadic predicate letter, without constants and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz -- among them, QK, QT, QKB, QD, QK4, and QS4.Comment: Pre-final version of the paper published in Studia Logica,doi:10.1007/s11225-018-9815-

De Re Updates

In this paper, we propose a lightweight yet powerful dynamic epistemic logic that captures not only the distinction between de dicto and de re knowledge but also the distinction between de dicto and de re updates. The logic is based on the dynamified version of an epistemic language extended with the assignment operator borrowed from dynamic logic, following the work of Wang and Seligman (Proc. AiML 2018). We obtain complete axiomatizations for the counterparts of public announcement logic and event-model-based DEL based on new reduction axioms taking care of the interactions between dynamics and assignments.Comment: In Proceedings TARK 2021, arXiv:2106.1088

АКСИОМАТИЗИРУЕМОСТЬ НЕНОРМАЛЬНЫХ И КВАЗИНОРМАЛЬНЫХ МОДАЛЬНЫХ ПРЕДИКАТНЫХ ЛОГИК ПЕРВОПОРЯДКОВО ОПРЕДЕЛИМЫХ КЛАССОВ ШКАЛ КРИПКЕ

Рассматривается вопрос о возможности эффективного описания ненормальных и квазинормальных предикатных модальных логик, определяемых семантически посредством классов шкал Крипке с выделенными мирами. Доказывается, что любая ненормальная или квазинормальная (в т. ч. нормальная) модальная предикатная логика, полная относительно некоторого первопорядково определимого класса шкал Крипке с выделенными мирами, погружается в классическую логику предикатов. Показано, как построить соответствующее погружение, используя т. н. стандартный перевод модальных предикатных формул в формулы языка классической логики предикатов. В конце работы приводятся следствия указанного результата, а также демонстрируются возможности обобщения описанной конструкции на классы других систем, в частности, на классы полимодальных логик — темпоральных логик с парой модальностей «всегда было» и «всегда будет» и логик знания с оператором распределенного знания. Показаны некоторые границы применимости описанного метода, приведены соответствующие примеры. Указаны контрпримеры, когда условия применимости метода для полной по Крипке модальной предикатной логики не выполнены, а построение эффективного описания этой логики, тем не менее, возможн

Vagueness in Predicates and Objects

Standard first-order logic interprets reference, predication and quantification in terms of fixed denotations with respect to a domain of precise objects. We explore ways to generalise this semantics to account for variability of meaning due to factors such as vagueness, context and diversity of definitions or opinions. We present Variable Reference Logic (VRL), an elaboration of Standpoint Logic, which is a multi-modal logic based on a variety of Supervaluation Semantics. VRL can accommodate several modes of variability in relation to both predicates and objects. Its principal novelty is that its semantics incorporates a domain of indefinite individuals, whose precise properties (such as spatial extension) are not fully determinate. Each indefinite individual is associated with a set of precise entities corresponding to possible precise versions of the individual

A PSpace Tableau Algorithm for Acyclic Modalized ALC

We study ALCK_m, which extends the description logic ALC by adding modal operators of the basic multi-modal logic K_m. We develop a sound and complete tableau algorithm Lambda_K for answering ALCK_m queries w.r.t. an ALCK_m knowledge base with an acyclic TBox. Defining tableau expansion rules in the presence of acyclic definitions by considering only the concept names on the left-hand side of TBox definitions or their negations, we are able to give a PSpace implementation for Lambda_K. We next consider answering ALCK_m queries w.r.t. an ALCK_m knowledge base in which the epistemic operators correspond to those of classical multi-modal logic S4_m. The expansion rules in the tableau algorithm Lambda_{S4} are designed to syntactically incorporate the epistemic properties. We also provide a PSpace implementation for Lambda_{S4}. In light of the fact that the satisfiability problem for ALCK_m with general TBox and no epistemic properties (i.e., K_{ALC}) is NEXPTIME-complete, we conclude that ALCK_m offers computationally manageable and practically useful fragment of K_{ALC}

Decidable fragments of first-order temporal logics

Accepted versio

Quantified epistemic logics for reasoning about knowledge in multi-agent systems

AbstractWe introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes.The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge, MIT Press, 1995; L. Lamport, Time, clocks, and the ordering of events in a distributed system, Communication of the ACM 21 (7) (1978) 558–565], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems