Abstract
Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.
Highlights
Branching-time logics have traditionally played a major role in modelling nondeterministic theories about time
The essential difference between them is the interpretation of the future operator F in a tree-like representation of time
In Peircean semantics, F φ is read as “eventually in the future, on every history passing through the moment under consideration, φ will happen”
Summary
Branching-time logics have traditionally played a major role in modelling nondeterministic theories about time. The Ockhamist language counterpart of the branching aspect of time is a modal operator L that quantifies over the set of histories passing through the moment under consideration. The tense operators have a Peircean reading, but the implicit quantification over histories is restricted to the indistinguishability class under consideration As it is pointed out in [22], Ockhamist and Peircean semantics correspond to the limit cases of the I -tree semantics in which each (respectively, no) history passing through t is distinguishable at t from any other. A finite axiomatization with a non standard rule for such a language interpreted over bundled I -trees with indistinguishability relations is given This axiomatization is proved to be sound and strongly complete.
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