An LFI with a transparent truth predicate

PAILOS, FEDERICO MATÍAS; BARRIO, EDUARDO ALEJANDRO; SZMUC, DAMIÁN

Buenos Aires

Workshop; IV Workshop on Philosophy of Logic; 2015

Buenos Aires Logic Group-S.A.D.A.F.

We will present an LFI first order three-valued logic with a transparent truth predicate called ?MST?. MST avoids triviality and has wide expressive power. In particular, it can express a strong negation without turning trivial. The way it reaches that goal is by relaxing the conditions to get self-referentiality. In particular, with biconditionals that are equal to conjunctions of sentences that have a non-classical conditional as the main constant, we can build sentences that can be read as expressing in the language ?The Liar? or a ?Curry sentence?. We will present a disjunctive sequent system called ?LST?, and prove that MST is complete with respect to it. Finally, we will present MST?s non-triviality proof. MST matrix is non-monotonic, and this makes harder finding a fixed-point interpretation of the truth predicate, and thus proving the non-triviality of the theory. This proof will involve a cut-elimination proof for LST.