Computation of Fuzzy Truth Values for The Liar and Related Self-Referential Systems

The Liar and Related Paradoxes: Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

We study self-referential sentences of the type related to the Liar paradox. In particular, we consider the problem of assigning consistent fuzzy truth values to collections of self-referential sentences. We show that the problem can be reduced to the solution of a system of nonlinear equations. Furthermore, we prove that, under mild conditions, such a system always has a solution (i.e. a consi...

The Liar and Related Paradoxes: Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

On the use of fuzzy logic and learning automata optimization to resolve the Liar and related paradoxes

We show that logical paradoxes based on self-reference (of which the Liar is the best known example) are equivalent to the non-existence of solutions to a numerical system of equations, the so-called truth-value equations. Furthermore, we show that in many cases a self-referential system which does not posses a crisp (Boolean) solution can be solved by expanding the solution set to include fuzz...

Fuzzy Decisions in Modular Neural Networks

Modular neural networks structured as associative memories are capable of processing inputs built from tensorial products of vectors. In this context, the operators of propositional and modal logic can be represented as modular distributed memories that can process not only classical Boolean but also fuzzy evaluations of truth-values of sentences. Furthermore, projecting memory outputs onto uni...

Yablo’s Paradox and Kindred Infinite Liars

This is a defense and extension of Stephen Yablo’s claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form “None of these subsequent sentences are true” generates the same instability in assigning truth values. I argue Yablo’s technique of substituting infinity for self-reference applies to all so-called “self-referential” paradoxes...