In this paper we investigate the simple logical properties of contexts. We describe both the syntax and semantics of a general propositional language of context, and give a Hilbert style proof system for this language. A propositional logic of context extends classical propositional logic in two ways. Firstly, a new modality, ist(; OE), is introduced. It is used to express that the sentence, OE, holds in the context . Secondly, each context has its own vocabulary, i.e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are the soundness and completeness of this Hilbert style proof system. We also provide soundness and completeness results (i.e. correspondence theory) for various extensions of the general system.

We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classification of standard connectives via equations on consequence relations (these include Girard's "multiplicatives" and "additives"). We next investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as good representations in each case (especially from the implementation point of view) are explained. We end by briefly outlining (with examples) some methods for developing non-uniform, but still efficient, representations of consequence relations.

Explanation-Based Learning (EBL) is a widely-used technique for acquiring searchcontrol knowledge. Recently, Prieditis, van Harmelen, and Bundy pointed to the similarity between Partial Evaluation (PE) and EBL. However, EBL utilizes training examples whereas PE does not. It is natural to inquire, therefore, whether PE can be used to acquire searchcontrol knowledge, and if so at what cost? This paper answers these questions by means of a case study comparing prodigy/ebl, a state-of-the-art EBL system, and static, a PEbased analyzer of problem-space definitions. When tested in prodigy/ebl's benchmark problem spaces, static generated search-control knowledge that was up to three times as effective as the knowledge learned by prodigy/ebl, and did so from twenty-six to seventyseven times faster. The paper describes static's algorithms, compares its performance to prodigy/ebl's, noting when static's superior performance will scale up and when it will not. The paper concludes with several le...

) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@bell-labs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state spaces as partial Kripke structures, and give a 3-valued interpretation to modal logic formulas on these structures. The third truth value ? means "unknown whether true or false". We define a preorder on partial Kripke structures that reflects their degree of completeness. We then provide a logical characterization of this preorder. This characterization thus relates properties of less complete structures to properties of more complete structures. We present similar results for labeled transition systems and show a connection to intuitionistic modal logic. We also present a 3-valued CTL model checking algorithm, which returns ? only when the partial state space lacks information needed ...

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We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the model-checking problem for any 3-valued temporal logic can be reduced to two model-checking problems for the corresponding 2-valued temporal logic. We then introduce a new semantics for 3-valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula OE on a partial Kripke structure M returns the third truth value? (read "unknown") only if there exist Kripke structures M1 and M2 that both complete M and such that M1 satisfies OE while M2 violates OE, hence making the value of OE on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M wit...

An earlier, not yet conclusive, attempt at formulating a theory of this kind was made by Scott 1970. Also related, although less closely, are the type and logic free theories of constructions of Kreisel 1962 and 1965 and Goodman 1970. In its first version, the present theory was based on the strongly impredicative axiom that there is a type of all types whatsoever, which is at the same time a type and an object of that type. This axiom had to be abandoned, however, after it was shown to lead to a contradiction by Jean Yves Girard. I am very grateful to him for showing me his paradox. The change that it necessitated is so drastic that my theory no longer contains intuitionistic simple type theory as it originally did. Instead, its proof theoretic strength should be close to that of predicative analysis.

The motivation for this paper, the first in a planned series of three parts, is the multitude of concepts surrounding the proper definition of complex modeling languages for systems and software, and the confusion that this often causes.

this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in Sections 4 and 5, we discuss model theory and fixed points, which play a crucial role in the definition of semantics. Section 6 is the main section of the paper and is entirely devoted to a systematic exposition and comparison of various proposed semantics. In Section 7 we discuss the relationship between declarative semantics of deductive databases and logic programs and non-monotonic reasoning. Section 8 contains concluding remarks. 2 Deductive Databases