Related papers: On semantics of first-order justification logic wi…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Henkin, Monk and Tarski gave a compositional semantics for first-order predicate logic. We extend this work by including function symbols in the language and by giving the denotation of the atomic formula as a composition of the denotations…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Artificial Intelligence aims to provide computer programs with commonsense knowledge to reason about our world. This paper offers a new practical approach towards automated commonsense reasoning with first-order logic (FOL) ontologies. We…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
The Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic founded…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…