Mathematics – Logic
Scientific paper
2010-06-11
Annals of Pure and Applied Logic, Volume 161, Issue 6, March 2010, Pages 789-799 (The proceedings of the IPM 2007 Logic Confer
Mathematics
Logic
Scientific paper
10.1016/j.apal.2009.06.008
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; show that provability degree of a formula w.r.t. a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory (such as that of a probability space or an $L^p$ Banach lattice) is decidable.
Didehvar Farzad
Ghasemloo Kaveh
Pourmahdian Massoud
No associations
LandOfFree
Effectiveness in RPL, with Applications to Continuous Logic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Effectiveness in RPL, with Applications to Continuous Logic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effectiveness in RPL, with Applications to Continuous Logic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-76916