Bi-facial Truth: a Case for Generalized Truth Values

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semi-classical negations”. Each of these negations deals only with one of the above mentioned components, and they may be of use for a logical reconstruction of argumentative reasoning.     

A Few More Useful 8-valued Logics for Reasoning with Tetralattice <Emphasis Type="Italic">EIGHT</Emphasis><Subscript>4</Subscript>

In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN ₃ with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT ₄. Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a–order (truth order) and d–order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations (a–connectives and d–connectives) and consequence relation defined via a–ordering is considered. An adequate axiomatization for this logic is proposed.     

The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins

Journal of Philosophical Logic - In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic...