Related papers: Argumentative Characterizations of (Extended) Disj…
Adding interaction to logic programming is an essential task. Expressive logics such as linear logic provide a theoretical basis for such a mechanism. Unfortunately, none of the existing linear logic languages can model interactions with…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…
This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying…
Open logic programs and open entailment have been recently proposed as an abstract framework for the verification of incomplete specifications based upon normal logic programs and the stable model semantics. There are obvious analogies…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central…
We are aiming at a semantics of logic programs with preferences defined on rules, which always selects a preferred answer set, if there is a non-empty set of (standard) answer sets of the given program. It is shown in a seminal paper by…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…