Related papers: COOL 2 -- A Generic Reasoner for Modal Fixpoint Lo…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…
Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
We present Coalition Logic, a three-valued modal fixed-point logic designed for declaratively specifying and reasoning about distributed algorithms, such as the Paxos consensus algorithm. Our methodology represents a distributed algorithm…
We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of…
We extend concurrent game structures (CGSs) with a simple notion of preference over computations and define a minimal notion of rationality for agents based on the concept of dominance. We use this notion to interpret a CL and an ATL…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…