Fully fregean logics

• Autorzy: Babyonyshev S.
• Języki publikacji: EN

Abstrakty

EN

Frege's Principle asserts that the denotation of a propositional sentence coincides with its truth value. In the context of algebraizable logics the principle can be interpreted as the compositionality of interderivability relation \Fr{S}, defined formally by \Fr{S}T=\{\langle \phi, \psi\rangle\in\Fml^2\mid T,\phi \dashv\vdash_{\mathcal S}T,\psi \}, for given deductive system \mathcal S$ and any $\mathcal S$-theory $T$. Of special interest are the deductive systems for which the property of being Fregean is inherited by all full 2nd-order models, so called, \it{fully Fregean} deductive systems. The main result of this paper is a characterization of fully Fregean deductive systems over countable languages using properties of the strong Frege operator on the formula algebra. The example of a Fregean, but not fully Fregean deductive system $\mathcal S$ is provided. $\mathcal S$ also turns out to be selfextensional, but not fully selfextensional, and, in addition, the three principal algebraic semantics for $\mathcal S$ are different, i.e., $\Alg^\ast\mathcal S\subsetneq\Alg\mathcal S\subsetneq\Var(\Alg\mathcal S)$.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2003
• Tom: No. 37
• Strony: 59--77
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Babyonyshev S.

• 400, Carver Hall, Iowa State University, Ames, Iowa, 50011, USA,

Bibliografia

• [1] R. Suszko, Ontology in the tractatus of l. wittgenstein, Notre Dame J. Formal Logic 9 (1968), no. 7, 33.
• [2] — Identity connective and modality, Studia Logica 27 (1971), no. 7, 41.
• [3] J. Czelakowski, Protoalgebraic logics, Kluwer, Dordrecht, 2001.
• [4] J. Czelackowski and D. Pigozzi, Fregean logics, Tech. Report 00–14, Iowa State University of Science and Technology, Department of Mathematics, 2000.
• [5] J. M. Font and R. Jansana, A general algebraic semantics for sentential logics, Number 7 in Lecture Notes in Logic, Springer-Verlag, 1996.
• [6] R. Jansana J.M. Font and D. Pigozzi, Fully adequate gentzen systems and the deduction theorem, Tech. Report 99–15, Iowa State University of Science and Technology, Department of Mathematics, 1999.