Systems of connexive logic are motivated by ideas of coherence or connection between premises and conclusions of valid inferences. The kind of coherence concerns the meaning of implication and negation. This is typical of the school of Relevance Logic, spearheaded by Anderson and Belnap, amongst others. It also appears earlier on on the work of D. Nelson on ``strong negation". Proof theorists eschew work on this kind of logic system, deeming it ad hoc and not mathematical enough, given the lack of proof systems for these logics with good properties such as substitutivity, cut-elimination, analyticity and such like.
Meanwhile a large amount of work is underway in more applied Computational Semantics trying to pin down notions of ``textual inference" as described for instance by Dagan et al in the RTE competitions. The textual inference problem consists of given two pieces of text, the hypothesis {\bf H} and the thesis {\bf T}, one needs to decide whether the hypothesis implies the thesis (entailment detection), whether the hypothesis is contradictory with the thesis (contradiction detection) or whether we cannot assert either entailment or contradiction between the texts (neutrality detection). Entailment for RTE differs from traditional mathematical logic entailment in that H entails T if the meaning of T can be inferred from the meaning of H as this would be typically interpreted by people: this informal definition is based on (and assumes) common human understanding of language, as well as common background knowledge.
This very preliminary talk attempts to connect connexive logic to an idealized system behind some of the more logically inspired work on textual inference, namely the work of MacCartney & Manning, Djalali, Icard and Moss. These more traditionally logic works on textual inference are extensions of Aristotle's syllogisms, where the notion of implication is relevant. We discuss a system which is intuitionistic and an idealized version of the logic (ECD for Entailment and Contradiction Detection) of the PARC Bridge system.
School of Informatics and Computing, Indiana University.