On finitely recursive programs

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 model semantics is highly undecidable. In this paper we prove that a larger class of programs, called finitely recursive programs, preserves most of the good properties of finitary programs under the stable model semantics, namely: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: We prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting omega-sequence converge to a stable model of P.Comment: 26 pages, Preliminary version in Proc. of ICLP 2007, Best paper awar

Introduction—What is Epistemic Contextualism?

Introduces contextualism about knowledge ascriptions, and provides a brief summary of the contributions to the Routledge Handbook of Epistemic Contextualism

A decidable subclass of finitary programs

Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs

A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature