DEDUCTION IN TIL: FROM SIMPLE TO RAMIFIED HIERARCHY OF TYPES

• Authors: Marie Duží
• Languages of publication: EN

Abstracts

EN

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First the author briefly recapitulates the rules of simple-typed calculus as presented by Tichý. Then she proposes the adjustments of the calculus so that it will be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. She shows that operating in a hyperintensional context is far from being technically trivial. Yet it is feasible. To this end we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions.

Keywords

EN

EXTENSIONAL RULES; HYPERINTENSIONS; SEQUENT CALCULUS; SUBSTITUTION; TICHÝ; TRANSPARENT INTENSIONAL LOGIC

• Publisher: Institute of Philosophy of the Slovak Academy of Sciences and Institute of Philosophy of Academy of Sciences of Czech Republic
• Journal: Organon F. medzinárodný časopis pre analytickú filozofiu
• Year: 2013
• Volume: 20
• Issue: suppl. 2
• Pages: 5 – 36

Contributors

author

Marie Duží

• Katedra počítačových věd, VSB-Technická Universita Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic