Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate high-level qualitative spatial information in a flexible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1st-order theories of certain spatial relations have been given [20]. But computing inferences in 1st-order logic is generally intractable unless special (domain dependent) methods are known. 0-order modal logics provide an alternative representation which is more expressive than classical 0-order logic and yet often more amenable to automated deduction than 1st-order formalisms. These calculi are usually interpreted as propositional logics: non-logical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand...

Normal modal logics can be defined axiomatically as Hilbert systems, or semantically in terms of Kripke's possible worlds and accessibility relations. Unfortunately there are Hilbert axioms which do not have corresponding first-order properties for the accessibility relation. For these logics the standard semantics-based theorem proving techniques, in particular, the relational translation into first-order predicate logic, do not work. There is an alternative translation, the so-called functional translation, in which the accessibility relations are replaced by certain terms which intuitively can be seen as functions mapping worlds to accessible worlds. In this paper we show that from a certain point of view this functional language is more expressive than the relational language, and that certain second-order frame properties can be mapped to first-order formulae expressed in the functional language. Moreover, we show how these formulae can be computed automatically from the ...

This paper deals with methods of faithful transformations between logical systems. Several methods for developing transformations of logical formulae are defined which eliminate unwanted properties from axiom systems without losing theorems. The elementary examples we present are permutation, transitivity, equivalence relation properties of predicates and congruence properties of functions. Various translations between logical systems are shown to be instances of K-transformations, for example the transition from relational to functional translation of modal logic into predicate logic, the transition from axiomatic specifications of logics via unary provability relations to a binary consequence relations, and the development of neighbourhood semantics for nonclassical propositional logics. Furthermore we show how to eliminate self resolving clauses like the condensed detachment clause, resulting in dramatic improvements of the performance of automated theorem provers on extremely hard ...

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