The Logic of Location |
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| Authors: | Peter Simons |
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| Institution: | (1) School of Philosophy, University of Leeds, Leeds, LS2 9JT, UK |
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| Abstract: | I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of
Prior. We have a collection L of locations and a collection S of statements such that a statement may be evaluated for truth at each location. Typically one and the same statement may
be true at one location and false at another. Given this semantic framework we may proceed in two ways: introducing names
for locations, predicates for the relations among them and an “at” preposition to express the value of statements at locations;
or introduce statement operators which do not name locations but whose truth-conditional effect depends on the truth or falsity
of embedded statements at various locations. The latter is akin to Prior’s approach to tense logic. In any logic of location
there will be some basic operators which we can define. By ringing the changes on the topology of locations, different logical
systems may be generated, and the challenge for the logician is then in each case to find operators, axioms and rules yielding
a proof theory adequate to the semantics. The generality of the approach is illustrated with familiar and not so familiar
examples from modal, tense and place logic, mathematics, and even the logic of games.
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