NDLI: Transition Semantics for Branching Time

Content Provider	Springer Nature Link
Author	Rumberg, Antje
Copyright Year	2015
Abstract	In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the moment-history pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of so-called transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open at a branching point. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. In addition to temporal and modal operators, a so-called stability operator becomes interpretable as a universal quantifier over the possible future extensions of a given transition set. The stability operator allows us to specify how and how far time has to unfold for the truth value of a sentence at a moment to become settled and enables a perspicuous treatment of future contingents. We show that the semantics developed along those lines generalizes and extends extant approaches: both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only, and on both accounts, stability collapses into truth.
Starting Page	77
Ending Page	108
Page Count	32
File Format	PDF
ISSN	09258531
Journal	Journal of Logic, Language and Information
Volume Number	25
Issue Number	1
e-ISSN	15729583
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-11-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Branching time Transitions Stability Future contingents Logic Semantics Information Systems Applications (incl. Internet)
Content Type	Text
Resource Type	Article
Subject	Philosophy Computer Science Linguistics and Language

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