Weak theories of truth and explicit mathematics
نویسندگان
چکیده
We study weak theories of truth over combinatory logic and their relationship to weak systems of explicit mathematics. In particular, we consider two truth theories TPR and TPT of primitive recursive and feasible strength. The latter theory is a novel abstract truth-theoretic setting which is able to interpret expressive feasible subsystems of explicit mathematics.
منابع مشابه
Recent Progress in Formal Theories of Truth
Contemporary conceptions of truth can be divided into two broad categories: philosophical and logical ones. Admittedly the division is not sharp, nor it should be: philosophers need formal results and the logicians often take philosophical intuitions into account in their formal constructions. Any intuitive conception of truth has to pass the test of formalization in order to count as valid or ...
متن کاملRemarks on Compositionality and Weak Axiomatic Theories of Truth
The paper draws attention to an important, but apparently neglected distinction relating to axiomatic theories of truth, viz. the distinction between weakly and strongly truth-compositional theories of truth. The paper argues that the distinction might be helpful in classifying weak axiomatic theories of truth and examines some of them with respect to it.
متن کاملWeak hyper semi-quantales and weak hypervalued topological spaces
The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...
متن کاملElement of justification in contemporary epistemology
The definition of propositional knowledge has been said to be: "knowledge is belief in justified truth" and belief, truth, and justified are necessary and adequate conditions in the actualization of knowledge. Many faults have been directed towards this three elemental definition, which some of them have been derived from the element of justification. This article reviews some of the most im...
متن کاملA feasible theory of truth over combinatory algebra
We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that hav...
متن کامل