Epistemic Foundation of Stable Model Semantics

Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond-Lifschitz transformation. The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of `falsehood' to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming (TPLP

Methods of conceptual clustering and their relation to numerical taxonomy

Artificial Intelligence (AI) methods for machine learning can be viewed as forms of exploratory data analysis, even though they differ markedly from the statistical methods generally connoted by the term. The distinction between methods of machine learning and statistical data analysis is primarily due to differences in the way techniques of each type represent data and structure within data. That is, methods of machine learning are strongly biased toward symbolic (as opposed to numeric) data representations. We explore this difference within a limited context, devoting the bulk of our paper to the explication of conceptual clustering, an extension to the statistically based methods of numerical taxonomy. In conceptual clustering the formation of object clusters is dependent on the quality of 'higher-level' characterizations, termed concepts, of the clusters. The form of concepts used by existing conceptual clustering systems (sets of necessary and sufficient conditions) is described in some detail. This is followed by descriptions of several conceptual clustering techniques, along with sample output. We conclude with a discussion of how alternative concept representations might enhance the effectiveness of future conceptual clustering systems

Automatic Generation of Proof Tactics for Finite-Valued Logics

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful systems resides in their responsiveness to extensibility of their reasoning capabilities, being designed over rule-based programming languages that allow the user to build her own `programs to construct proofs' - the so-called proof tactics. The present contribution discusses the implementation of an algorithm that generates sound and complete tableau systems for a very inclusive class of sufficiently expressive finite-valued propositional logics, and then illustrates some of the challenges and difficulties related to the algorithmic formation of automated theorem proving tactics for such logics. The procedure on whose implementation we will report is based on a generalized notion of analyticity of proof systems that is intended to guarantee termination of the corresponding automated tactics on what concerns theoremhood in our targeted logics

Information-theoretic approach to quantum error correction and reversible measurement

Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive information-theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyze the thermodynamic cost of error correction and show that error correction can be regarded as a kind of ``Maxwell demon,'' for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.Comment: 31 pages, REVTEX, one figure in LaTeX, submitted to Proceedings of the ITP Conference on Quantum Coherence and Decoherenc