Stable Semantics of Temporal Deductive Databases

We define a preferential semantics based on stable generated models for a very general class of temporal deductive databases. We allow two kinds of temporal information to be represented and queried: timepoint and timestamp formulas, and show how each of them can be translated into the other. Because of their generality, our formalism and our semantics can serve as a basis for comparing and extending other temporal deductive database frameworks

Semi-Stable Semantics for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria that have been used to settle the acceptance of arguments are called semantics. However, the notion of semi-stable semantics as studied for abstract argumentation frameworks has received little attention for ADFs. In the current work, we present the concepts of semi-two-valued models and semi-stable models for ADFs. We show that these two notions satisfy a set of plausible properties required for semi-stable semantics of ADFs. Moreover, we show that semi-two-valued and semi-stable semantics of ADFs form a proper generalization of the semi-stable semantics of AFs, just like two-valued model and stable semantics for ADFs are generalizations of stable semantics for AFs

On the equivalence between logic programming semantics and argumentation semantics

This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

On the Equivalence between Logic Programming Semantics and Argumentation Semantics

Publisher PD

The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument. - The Center problem asks whether, given two extensions of distance k, whether there is a "center" extension that is a distance at most (k-1) from both given extensions. We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results covers several different semantics, including admissible, complete, preferred, semi-stable and stable semantics

Weakening the stable semantics

We report our research on semantics for normal/disjunctive programs. One of the most well known semantics for logic programming is the stable semantics (STABLE). However, it is well known that very often STABLE has no models. In this paper we study the stable semantics and present some new results about it. Furthermore, we introduce a new semantics (that we call D3-WFS-DCOMP) and compare it with STABLE. For normal programs, this semantics is based on a suitable integration of WFS and the Clark's Completion. D3-WFS-DCOM has the following appealing properties: First, it agrees with STABLE in the sense that it never defines a non minimal model or a non minimal supported model. Second, for normal programs it extends WFS. Third, every stable model of a disjunctive program P is a D3-WFS-DCOM model of $P$. Fourth, it is constructed using transformations accepted by STABLE. We also introduce a second semantics that we call D2-WFS-DCOMP. We show that D2-WFS-DCOMP is equivalent to D3-WFS-DCOMP for normal programs but this is not the case for disjunctive programs. We also introduce a third new semantics that insists in the use of implicit disjunctions. We briefly sketch how these semantics can be extended to programs including: explicit negation, default negation in the head of a clause, as well as a lub operator ( which is the generalization of setof over arbitrary complete lattices). We sketch how to model this lub operator using standard disjunctive clauses. However, we can not use the STABLE semantics but instead any of our suggested semantics. We emphasizes that the ultimate goal of our research is to understand better the STABLE semantics and to suggest solutions to the drawbacks of the stable semantics (that becomes undefined very often).Postprint (published version

Compact Argumentation Frameworks

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.Comment: Contribution to the 15th International Workshop on Non-Monotonic Reasoning, 2014, Vienn

Lambda theories of effective lambda models

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the more general question of whether the equational (resp. order) theory of a non syntactical model M, say Eq(M) (resp. Ord(M)) can be recursively enumerable (= r.e. below). We conjecture that no such model exists and prove the conjecture for several large classes of models. In particular we introduce a notion of effective lambda-model and show that for all effective models M, Eq(M) is different from Lb, and Ord(M) is not r.e. If moreover M belongs to the stable or strongly stable semantics, then Eq(M) is not r.e. Concerning Scott's continuous semantics we explore the class of (all) graph models, show that it satisfies Lowenheim Skolem theorem, that there exists a minimum order/equational graph theory, and that both are the order/equ theories of an effective graph model. We deduce that no graph model can have an r.e. order theory, and also show that for some large subclasses, the same is true for Eq(M).Comment: 15 pages, accepted CSL'0