Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

What If? The Exploration of an Idea

Abstract: A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes.

Handling Uncertainty, Context, Vague Predicates, and Partial Inconsistency in Possibilistic Logic

Abstract: This short paper intends to provide an introduction to possibilistic logic, a logic with weighted formulas, to its various capabilities and to its potential applications. Possibilistic logic, initially proposed in [11], see also Lea Sombe [26] for an introduction, can be viewed as an important fragment of Zadeh[32]’ s possibility distribution-based theory of approximate reasoning, put in a logical form. Possibilistic logic also relies on an ordering relation reflecting the relative certainty of the formulas in the knowledge base. As it will be seen, its semantics is based on a possibility distribution which is nothing but a convenient encoding of a preference relation a la Shoham[29], between interpretations. This kind of semantics should not be confused with the similarity relation-based semantics recently proposed by Ruspini[28] for fuzzy logics which rather extends the idea of interchangeable interpretations in a coarsened universe, e.g. Farinas del Cerro and Orlowska[17], and which corresponds to another issue.