Challenging the Computational Metaphor: Implications for How We Think

This paper explores the role of the traditional computational metaphor in our thinking as computer scientists, its influence on epistemological styles, and its implications for our understanding of cognition. It proposes to replace the conventional metaphor--a sequence of steps--with the notion of a community of interacting entities, and examines the ramifications of such a shift on these various ways in which we think

On cascade products of answer set programs

Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or "emulated") by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.Comment: Appears in Theory and Practice of Logic Programmin

A generic framework for the analysis and specialization of logic programs

The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In this work we present what we argüe is the first fully described generic algorithm for efñcient and precise integration of abstract interpretation and partial deduction. Taking as starting point state-of-the-art algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial deduction, we present an algorithm which combines the best of both worlds. Key ingredients include the accurate success propagation inherent to abstract interpretation and the powerful program transformations achievable by partial deduction. In our algorithm, the calis which appear in the analysis graph are not analyzed w.r.t. the original definition of the procedure but w.r.t. specialized definitions of these procedures. Such specialized definitions are obtained by applying both unfolding and abstract executability. Our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of such parameters correspond to existing algorithms for program analysis and specialization. Simultaneously, our approach opens the door to the efñcient computation of strictly more precise results than those achievable by each of the individual techniques. The algorithm is now one of the key components of the CiaoPP analysis and specialization system

On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical Frameworks

We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional signature using only atoms from that signature. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014