A System of Temporal Logic with Operators of Contingency

(Logik & Philosophie der Mathematik, Englisch)

ollowing a tradition of study that begins with Montgomery and Routley in the Sixties, we consider a logic with primitive operators of contingency. More precisely, we explore the use of an operator of past contingency and an operator of future contingency in a system S of temporal logic whose language includes a propositional constant.

Given the axiomatic basis for S, we prove that:

(i) the usual operators of past necessity and future necessity are definable in S by means of the propositional constant and our primitive operators;

(ii) S is sound and complete with respect to a class C of temporal models.

Each model in C is defined as a 4-tuple (T, <,>, v) where T is a non-empty set of instants t; < is the temporal relation "before" (t<t' means that t is before t'), > is the temporal relation "after" (t>t' means that t is after t') and v is a valuation function assigning to every atomic formula of the language the set of instants at which that formula is true. We also prove that our axiomatic basis for S grants a fundamental intuition about temporal series, ie. the fact that < and > are reciprocally converse (if t<t' then t'>t and the other way round). According to Arthur Prior, this property is required for every normal system of temporal logic.

References:

- Kuhn (1995). Minimal Non-contingency Logic. Notre Dame Journal of Formal Logic 36, 230-234.

- Montgomery & Routley (1966). Contingency and Non-contingency Bases for Normal Modal Logics. Logique et Analyse 9, 318-328.

- Pizzi (2007) Necessity and Relative Contingency. Studia Logica 85, 395-410.

Chair: Christine Schurz

Zeit: 09:45-10:15, 14. September 2013 (Samstag)

Ort: HS 104

Matteo Pascucci

(University of Verona, Italien)

Matteo Pascucci, PhD student in Computer Science (University of Verona). 2012 Master's degree in Philosophy as a member of the Honours College "Bernardo Clesio" (University of Trento); 2010 Bachelor's degree in Philosophy (University of Siena). Areas of interest: Logic, Philosophy of Language, Philosophy of Time.

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