connexive

Since classical propositional logic is Post-complete, any additional axiom in its language gives rise to the trivial system, so that any non-trivial system of connexive logic will have to leave out some theorems of classical logic.

Connexive Logic Wansing, Heinrich 2006

Since every non-trivial system of connexive logic has to omit some classical tautologies, and since the standard paradoxes of non-relevant, material implication can be avoided by rejecting Conjunctive Simplification, i.e.,

Connexive Logic Wansing, Heinrich 2006

Although the semantics of Priest's connexive logics is simple and transparent, the underlying idea of subtraction negation is not unproblematic.

Connexive Logic Wansing, Heinrich 2006

In the late 1970s and the 1980s, connexive logic was subjected to semantical investigations based on ternary frames for relevance logics.

Connexive Logic Wansing, Heinrich 2006

Moreover, McCall points out that CC1 has some properties that are difficult to justify, if the name ˜connexive logic™ is meant to reflect the fact that in a valid implication

Connexive Logic Wansing, Heinrich 2006

Examples of non-trivial inconsistent systems of connexive logic satisfying Conjunctive Simplification are presented in Sections 1.4 and 1.5.

Connexive Logic Wansing, Heinrich 2006

Routley requires for a connexive logic the rejection or qualification of Conjunctive Simplification (or equivalent schemata).

Connexive Logic Wansing, Heinrich 2006

The connection between the subtraction account of negation and the principles distinctive of connexive logic is explained by Routley and Routley (1985, p. 205) as follows:

Connexive Logic Wansing, Heinrich 2006

In Wansing 2007 connexive implication is motivated by introducing a negation connective into Categorial Grammar in order to express negative information about membership in syntactic categories.

Connexive Logic Wansing, Heinrich 2006

There are several kinds of systems of connexive logics with different kinds of semantics and proof systems.

Connexive Logic Wansing, Heinrich 2006