We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] that is sound for the sceptical grounded semantics

No abstract

No abstract

Modularity is a key issue in the design of modern programming languages. When designing modular features for declarative languages in general, and for logic programming languages in particular, the challenge lies in avoiding the superimposition of a complex syntactic and semantic structure over the simple structure of the basic language. The modular framework defined here for logic programming consists of a small number of operations over modules which are (meta-) logically defined and semantically justified in terms of the basic logic programming semantics. The operations enjoy a number of algebraic properties, thus yielding an algebra of modules. Despite its simplicity, the suite of operations is shown capable of capturing the core features of modularization: information hiding, import/export relationships, and construction of module hierarchies. A metalevel implementation and a compilation-oriented implementation of the operations are provided and proved sound with respect to the semantics. The compilation-oriented implementation is based on manipulation of name spaces and provides the basis for an efficient implementation.

We provide a simple formulation of a framework where some extensions of logic programming with non-monotonic reasoning are treated uniformly, namely, two kinds of negation and abduction. The resulting semantics is purely model-theoretic, and gives meaning to any noncontradictory abductive logic program. Moreover, it embeds and generalizes some existing semantics which deal with negation and abduction, The framework is equipped with a correct top-down proof procedure