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Transition Semantics for Branching Time.
1Department of Philosophy, University of Konstanz, Postfach 17, 78457 Konstanz, Germany.
Journal of Logic, Language, and Information
|April 13, 2016
Summary
We introduce a new propositional semantics using branching time and transitions, offering a more detailed view of modality and time. This approach enhances the understanding of future contingents and generalizes existing theories.
Area of Science:
- Philosophy of Time
- Modal Logic
- Formal Semantics
Background:
- Standard Ockhamist semantics uses moment-history pairs for truth.
- Branching time frameworks model alternative possible futures.
- Existing semantics struggle with incomplete future possibilities.
Purpose of the Study:
- Develop a novel propositional semantics based on branching time.
- Introduce a 'transition semantics' to model incomplete future parts.
- Provide a fine-grained analysis of modality and time.
Main Methods:
- Replace moment-history pairs with moment-transition set pairs.
- Utilize the structural properties of branching time.
- Define a 'stability' operator as a universal quantifier over future extensions.
Main Results:
- Transition semantics allows for incomplete future parts.
- The stability operator clarifies when future truth values become settled.
- Peirceanism and Ockhamism are shown as limiting cases of this approach.
Conclusions:
- The transition semantics offers a generalized framework for temporal and modal logic.
- It provides a perspicuous treatment of future contingents.
- This approach enhances the understanding of how time and modality interact.
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