David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 70 (4):1137 - 1149 (2005)
We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Vladimir Rybakov (2008). Decidability: Theorems and Admissible Rules. Journal of Applied Non-Classical Logics 18 (2-3):293-308.
V. Rybakov (2008). Linear Temporal Logic with Until and Next, Logical Consecutions. Annals of Pure and Applied Logic 155 (1):32-45.
Similar books and articles
Marcelo Finger & Dov M. Gabbay (1992). Adding a Temporal Dimension to a Logic System. Journal of Logic, Language and Information 1 (3):203-233.
Amílcar Sernadas, Cristina Sernadas & Carlos Caleiro (1997). Synchronization of Logics. Studia Logica 59 (2):217-247.
Andrzej Indrzejczak (2003). A Labelled Natural Deduction System for Linear Temporal Logic. Studia Logica 75 (3):345 - 376.
Mark Reynolds (1996). Axiomatising First-Order Temporal Logic: Until and Since Over Linear Time. Studia Logica 57 (2-3):279 - 302.
Heinrich Wansing & Norihiro Kamide (2011). Synchronized Linear-Time Temporal Logic. Studia Logica 99 (1-3):365-388.
V. V. Rybakov (1990). Logical Equations and Admissible Rules of Inference with Parameters in Modal Provability Logics. Studia Logica 49 (2):215 - 239.
Joeri Engelfriet & Jan Treur (2002). Linear, Branching Time and Joint Closure Semantics for Temporal Logic. Journal of Logic, Language and Information 11 (4):389-425.
Rajeev Goré (1994). Cut-Free Sequent and Tableau Systems for Propositional Diodorean Modal Logics. Studia Logica 53 (3):433 - 457.
Avi Sion (1990). Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities. Lulu.com.
Frank Wolter & Michael Zakharyaschev (2005). A Logic for Metric and Topology. Journal of Symbolic Logic 70 (3):795 - 828.
Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.
Added to index2010-08-24
Total downloads3 ( #284,287 of 1,096,899 )
Recent downloads (6 months)1 ( #273,368 of 1,096,899 )
How can I increase my downloads?