Interpolation Is (Not Always) Easy to Spoil

We study a version of the Craig interpolation theorem as formulated in the framework of the theory of institutions. This formulation proved crucial in the development of a number of key results concerning foundations of software specification and formal development. We investigate preservation of interpolation under extensions of institutions by new models and sentences. We point out that some interpolation properties remain stable under such extensions, even if quite arbitrary new models or sentences are permitted. We give complete characterisations of such situations for institution extensions by new models, by new sentences, as well as by new models and sentences, respectively

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

PROLOG META-INTERPRETERS FOR RULE-BASED INFERENCE UNDER UNCERTAINTY

Uncertain facts and inexact rules can be represented and processed in standard Prolog through meta-interpretation. This requires the specification of appropriate parsers and belief calculi. We present a meta-interpreter that takes a rule-based belief calculus as an external variable. The certainty-factors calculus and a heuristic Bayesian belief-update model are then implemented as stand-alone Prolog predicates. These, in turn, are bound to the meta-interpreter environment through second-order programming. The resulting system is a powerful experimental tool which enables inquiry into the impact of various designs of belief calculi on the external validity of expert systems. The paper also demonstrates the (well-known) role of Prolog meta-interpreters in building expert system shells.Information Systems Working Papers Serie

What Is a Good Domain Description? Evaluating & Revising Action Theories in Dynamic Logic

Traditionally, consistency is the only criterion for the quality of a theory in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the meta-theory of actions by investigating what other properties a good domain description should satisfy. Having Propositional Dynamic Logic (PDL) as background, we state some meta-theoretical postulates concerning this sore spot. When all postulates are satisfied, we call the action theory modular. We point out the problems that arise when the postulates about modularity are violated, and propose algorithmic checks that can help the designer of an action theory to overcome them. Besides being easier to understand and more elaboration tolerant in McCarthy's sense, modular theorieshave interesting computational properties. Moreover, we also propose a framework for updating domain descriptions and show the importance modularity has in action theory change

A query-based approach to ontologies using the theory of institutions

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