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Realizability asks whether there exists a program satisfying its specification. In this problem, we assume that each agent has her own objective and behaves rationally to satisfy her objective. Traditionally, the rationality of agents is…
We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…
Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the…
In this paper we introduce a simple modal logic framework to reason about the expertise of an information source. In the framework, a source is an expert on a proposition $p$ if they are able to correctly determine the truth value of $p$ in…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
Over the course of the last 50 years, many questions in the field of computability were left surprisingly unanswered. One example is the question of $P$ vs $NP\cap co-NP$. It could be phrased in loose terms as "If a person has the ability…
Realizability for knowledge representation formalisms studies the following question: given a semantics and a set of interpretations, is there a knowledge base whose semantics coincides exactly with the given interpretation set? We…
We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…
Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…
We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
In modern industry, dynamic environments and the complexity of modular and reconfigurable resources require automated planning of process sequences. Capability-based planning approaches address this by automatically generating plans from…
In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…
Coalition logic is one of the most popular logics for multi-agent systems. While epistemic extensions of coalition logic have received much attention, existence of their complete axiomatisations has so far been an open problem. In this…
We study the multiagent epistemic logic CMAELCD with operators for common and distributed knowledge for all coalitions of agents. We introduce Hintikka structures for this logic and prove that satisfiability in such structures is equivalent…
Arbitrary Public Announcement Logic with Common Knowledge (APALC) is an extension of Public Announcement Logic with common knowledge modality and quantifiers over announcements. We show that the satisfiability problem of APALC on S5-models,…
Neural networks for NLP are becoming increasingly complex and widespread, and there is a growing concern if these models are responsible to use. Explaining models helps to address the safety and ethical concerns and is essential for…
We propose a calculus of string diagrams to reason about satisfiability of Boolean formulas, and prove it to be sound and complete. We then showcase our calculus in a few case studies. First, we consider SAT-solving. Second, we consider…