Logic Journal of IGPL - current issue

Extended semantics and inference for the Independent Choice Logic

Riguzzi, F. — Tue, 17 Nov 2009 07:48:50 PST

The Independent Choice Logic (ICL), proposed by Poole, is a language for expressing probabilistic information in logic programming that adopts a distribution semantics: an ICL theory defines a distribution over a set of normal logic programs. The probability of a query is then given by the sum of the probabilities of the programs where the query is true.

The ICL semantics requires the theory to be acyclic. This is a strong limitation that rules out many interesting programs. In this paper we present an extension of the ICL semantics that allows theories to be modularly acyclic.

Inference with ICL can be performed with the Ailog2 system that computes explanations to queries and then makes them mutually incompatible by means of an iterative algorithm.

We propose the system PICL (for Probabilistic inference with ICL) that computes the explanations to queries by means of a modification of SLDNF-resolution and then makes the explanations mutually incompatible by means of Binary Decision Diagrams.

PICL and Ailog2 are compared on problems that involve computing the probability of a connection between two nodes in biological graphs and in social networks. Moreover, they are also applied to three games of dice.

The problems considered are easily expressible in P-log, a probabilistic language based on Answer Set Programming. Therefore, the Plog system was also applied to the programs.

PICL was able to handle larger problems than Ailog2 and Plog. Moreover, it was the fastest of the three algorithms except for one case of one of dice games.

Modelling evolvable component systems: Part I: A logical framework

Barringer, H., Gabbay, D., Rydeheard, D. — Tue, 17 Nov 2009 07:48:50 PST

We develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level in the component hierarchy allowing us to use evolutionary behaviour as an integral part of system design.

We model such systems in a revision-based first-order logical framework in which supervisors are modelled as theories which are at a logical meta-level to the theories of their components. This enables evolutionary change of the component to be induced by revision-based changes of the supervisor at the meta-level. In this way, the intervention required in evolutionary change is modelled purely logically.

The hierarchical component-based structure is fairly intricate so we present the basic ideas firstly in a simple setting, the well-known blocks world, before introducing tree-based structures to represent component hierarchies. We also introduce some techniques for establishing the behaviour of evolvable systems specified in this logical framework. The ideas and concepts are driven by example throughout. We conclude with a more substantial example, that of a simple model of an evolvable system of automated bank teller machines.

Explicit substitutions calculi with one step Eta-reduction decided explicitly

Ventura, D., Ayala-Rincon, M., Kamareddine, F. — Tue, 17 Nov 2009 07:48:50 PST

It has long been argued that the notion of substitution in the -calculus needs to be made explicit. This resulted in many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions have been atomised. In contrast to the great variety of developments for making explicit formalisations of the Beta rule, less work has been done for giving explicit definitions of the conditional Eta rule. In this paper constructive Eta rules are proposed for both the - and the s_e-calculi of explicit substitutions. Our results can be summarised as follows: 1) we introduce constructive and explicit definitions of the Eta rule in the - and the s_e-calculi, 2) we prove that these definitions are correct and preserve basic properties such as subject reduction. In particular, we show that the explicit definitions of the eta rules coincide with the Eta rule for pure -terms and that moreover, their application is decidable in the sense that Eta redices are effectively detected (and contracted). The formalisation of these Eta rules involves the development of specific calculi for explicitly checking the condition of the proposed Eta rules while constructing the Eta contractum.

Independence-friendly cylindric set algebras

Mann, A. L. — Tue, 17 Nov 2009 07:48:50 PST

Independence-friendly logic (IF logic) is a conservative extension of first-order logic that has the same expressive power as existential second-order logic. We attempt to algebraize IF logic in the same spirit as cylindric algebra.

We define independence-friendly cylindric set algebras (IF algebras) and investigate to what extent they satisfy the axioms of cylindric algebra. We ask whether the equational theory of IF algebras is finitely axiomatizable, and prove two partial results. First, every IF algebra over a structure is an expansion of a Kleene algebra. Moreover, the class of such Kleene algebras generates the variety of all Kleene algebras. Second, every one-dimensional IF algebra over a structure is an expansion of a monadic Kleene algebra. However, the class of such monadic Kleene algebras does not generate the variety of all monadic Kleene algebras.¹

Neat reducts and amalgamation in retrospect, a survey of results and some methods Part II: Results on amalgamation

Madarasz, J., Ahmed, T. S. — Tue, 17 Nov 2009 07:48:50 PST

Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the (seemingly very innocent) fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new unpublished results (answering long-standing open problems in the field) concerning neat reducts and amalgamation are given. (Theorems 11, 13, 19 and 31-38 are such). Several counterexamples which convey the gist of techniques used in this area are presented two of which are new (Theorem 19, Theorem 38.) It is known that the algebraic notion of amalgamation in a class of algebras corresponds to the metalogical notion of interpolation in the corresponding logic. Answers to open question in the recent paper [31] concerning both amalgamation and interpolation are summarized in tabular form at the end of this paper.

This paper appears in two parts. The first part contains results on neat reducts. The present second part contains results relating the notion of neat embeddings to various amalgamation properties.¹

Erratum to "The Ricean Objection: An Analogue of Rice's Theorem for First-Order Theories" * Logic Journal of the IGPL, 16(6): 585-590(2008)

Oliveira, I. C., Carnielli, W. — Tue, 17 Nov 2009 07:48:50 PST

16th Workshop on Logic, Language, Information and Computation (WoLLIC 2009)

Tue, 17 Nov 2009 07:48:51 PST

Acknowledgements

Tue, 17 Nov 2009 07:48:51 PST