Abstract dialectical frameworks (ADFs) are a powerful generalization of Dung’s abstract argumentation frameworks. ADFs allow to model argumentation scenarios such that ADF semantics then provide interpretations of the scenarios. Among the considerable number of ADF semantics, the naive-based ones are built upon the fundamental concept of conflict-freeness. Intuitively, a three-valued interpretation of an ADF’s statements is conflict-free iff all true statements can possibly be accepted, and all false statements cannot possibly be accepted. In this paper, we perform an exhaustive analysis of the computational complexity of naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.

Combined approaches have become a successful technique for CQ answering over ontologies. Existing algorithms, however, are restricted to the logics underpinning the OWL 2 profiles. Our goal is to make combined approaches applicable to a wider range of ontologies. We focus on RSA: a class of Horn ontologies that extends the profiles while ensuring tractability of standard reasoning. We show that CQ answering over RSA ontologies without role composition is feasible in NP. Our reasoning procedure generalises the combined approach for ELHO and DL-LiteR using an encoding of CQ answering into fact entailment w.r.t. a logic program with function symbols and stratified negation. Our results have significant practical implications since many out-of-profile Horn ontologies are RSA.

We add epistemic modal operators to the language of here-and-there logic and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from here-and-there models by the standard minimisation of truth of Pearce’s equilibrium logic; they provide an epistemic extension of that logic. The latter are obtained from the former by maximising the set of epistemic possibilities; they provide a new semantics for Gelfond’s epistemic specifications.

In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Recently, Fang and Liu extended the situation calculus to account for multi-agent knowledge and belief change. In this paper, based on their framework, we investigate progression of both belief and knowledge in the single-agent propositional case. We first present a model-theoretic definition of progression of knowledge and belief. We show that for propositional actions, i.e., actions whose precondition axioms and successor state axioms are propositional formulas, progression of knowledge and belief reduces to forgetting in the logic of knowledge and belief, which we show is closed under forgetting. Consequently, we are able to show that for propositional actions, progression of knowledge and belief is always definable in the logic of knowledge and belief.

Justification logic originated from the study of the logic of proofs.  However, in a more general setting, it may be regarded as a kind of explicit epistemic logic. In such logic, the reasons why a fact is believed are explicitly represented as justification terms.  Traditionally, the modeling of uncertain beliefs is crucially important for epistemic reasoning. While graded modal logics interpreted with possibility theory semantics have been successfully applied to the representation and reasoning of uncertain beliefs, they cannot keep track of the reasons why an agent believes a fact. The objective of this paper is to extend the graded modal logics with explicit justifications. We introduce a possibilistic justification logic,  present its syntax and semantics, and investigate its meta-properties, such as soundness, completeness, and realizability.

We propose a versatile framework for combining knowledge bases in modular systems with preferences. In our formalism, each module (knowledge base) can be specified in a different language. We define the notion of a preference-based modular system that includes a formalization of meta-preferences. We prove that our formalism is robust in the sense that the operations for combining modules preserve the notion of  a preference-based modular system. Finally, we formally demonstrate correspondences between our framework and the related preference formalisms of cp-nets and preference-based planning. Our framework allows one to use  these preference formalisms (and others) in combination, in the same modular system.

The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the XXth century, and advocated as being of interest for understanding conceptual structures and solving problems in paraconsistent logics, the square of opposition has been recently completed into a cube, which corresponds to the introduction of a third negation. Such a cube can be encountered in very different knowledge representation formalisms, such as modal logic, possibility theory in its all-or-nothing version, formal concept analysis, rough set theory and abstract argumentation. After restating these results in a unified perspective, the paper proposes a graded extension of the cube and shows that several qualitative, as well as quantitative formalisms, such as Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belief functions and Choquet integrals, are amenable to transformations that form graded cubes of opposition. This discovery leads to a new perspective on many knowledge representation formalisms, laying bare their underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight some missing components present in one formalism and currently absent from another.

Argumentation is an inherently dynamic process. Given that argumentation can be viewed as a process as well Consequently, recent years have witnessed tremendous as a product, recent years have seen an increasing number of research efforts towards an understanding of studies on different problems in the dynamics of argumentation how the seminal AGM theory of belief change can frameworks [Baumann, 2012; Bisquert et al., 2011; 2013; be applied to argumentation, in particular for Dung's Boella et al., 2009; Booth et al., 2013; Cayrol et al., 2010; abstract argumentation frameworks (AFs). However, Doutre et al., 2014; Kontarinis et al., 2013; Krümpelmann et none of the attempts has yet succeeded in handling al., 2012; Nouioua and Würbel, 2014; Sakama, 2014]. The the natural situation where the revision of an AF is problem we tackle here is how to revise an AF when some new guaranteed to be representable by an AF as well.

We study the problem of aggregation of Dung's abstract argumentation frameworks. Some operators for this aggregation have been proposed, as well as some rationality properties for this process. In this work we study the existing operators and new ones that we propose in light of the proposed properties, highlighting the fact that existing operators do not satisfy a lot of these properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem also too demanding.

In this paper we present a theory of qualitative probability. Work in the area goes back at least to de Finetti. The usual approach is to specify a binary operator ≼ with φ ≼ ψ having the intended interpretation that φ is not more probable than ψ . We generalise these approaches by extending the domain of the operator ≼ from the set of events to the set of finite sequences of events. If Φ and Ψ are finite sequences of events, Φ ≼ Ψ has the intended interpretation that the summed probabilities of the elements of Φ is not greater than the sum of those of Ψ . We provide a sound and complete axiomatisation for this operator over finite outcome sets, and show that this theory is sufficiently powerful to capture the results of axiomatic probability theory. We argue that our approach is simpler and more perspicuous than previous accounts. As well, we prove that our approach generalises the two major accounts for finite outcome sets.