The indefinite two-valued Boolean function

Boolean-valued Term Models

We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

Pseudo-Boolean valued prolog

Logic programming has generally been developed in a Classical two-valued setting; there are no “degrees of truth”. What we propose here is the introduction of more general spaces of truth values, reading truth values as “evidence factors”. Then conventional logic programming may be seen as the special case in which only total evidence is acceptable, and so the space of evidences degenerates to ...

Boolean-Valued Models and Forcing

This introduction to forcing is based on Chapters 5–6 in T. J. Jech’s book The Axiom of Choice and is written primarily for the Fraenkel-Mostowski Models reading group. Forcing is introduced via Boolean-valued models and generic extensions, and these techniques are used to prove the independence of the axiom of choice of ZF. This is then related back to the theory of FM models. Please inform me...

A Boolean-valued probability theory

New foundations for probability theory are suggested and investigated, derived from the formalized systems theory and using also some other branches of mathematical logic. The probability measures are supposed to take their values not in the unit interval of reals, but in a special kind of Boolean algebras. Some analogies as well as differences of this approach with respect to the classical Kol...

Boolean-Valued Second-Order Logic