Related papers: Decidability of an Expressive Description Logic wi…
Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational…
State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a…
In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web. Specifically, we introduce the description logic $\mathcal{DL}\langle…
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
This paper concerns a goal directed proof procedure for the propositional fragment of the adaptive logic ACLuN1. At the propositional level, it forms an algorithm for final derivability. If extended to the predicative level, it provides a…
Reasoning is a fundamental capability of AI agents. Recently, large language models (LLMs) have shown remarkable abilities to perform reasoning tasks. However, numerous evaluations of the reasoning capabilities of LLMs have also showed some…
The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…
The Semantic Web effort has steadily been gaining traction in the recent years. In particular,Web search companies are recently realizing that their products need to evolve towards having richer semantic search capabilities. Description…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning…
We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form…
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…