Classical logic is embedded into constructive logic, through a definition of the classical connectives and quantifiers in terms of the constructive ones. The history of the notion of constructivity started with a dispute on the deduction rules that one should or should not use to prove a theorem. Depending on the rules accepted by the ones and the others, the proposition P ∨ ¬P , for instance, ...

The introduction of unary connectives has proved to be an important addition to the categorial vocabulary. The connectives considered so far are order-preserving; in this paper instead, we consider the addition of order-reversing, Galois connected operators. In §2 we do the basic model-theoretic and proof-theoretic groundwork. In §3 we use the expressive power of the Galois connected operators ...

Logical connectives on fuzzy sets arise from those on the unit interval. The basic theory of these connectives is cast in an algebraic spirit with an emphasis on equivalence between the various systems that arise. Special attention is given to De Morgan systems with strict Archimedean t-norms and strong negations. A typical result is that any De Morgan system with strict t-norm and strong negat...

We look at the average frequency of contrastive connectives in the SPaRKy Restaurant Corpus with respect to realization ratings by human judges. We implement a discriminative n-gram ranker to model these ratings and analyze the resulting n-gram weights to determine if our ranker learns this distribution. Surprisingly, our ranker learns to avoid contrastive connectives. We look at possible expla...

Abstract. With respect to discourse organisation, the most basic way of signalling the speaker’s or writer’s intentions is to use explicit lexical markers: so-called discourse markers or discourse connectives. While a lexicon of discourse connectives associated with the relations they express can be very useful for researchers, especially in Natural Language Processing, few projects aim at coll...