The challenge of giving a semantics for relevance logic in terms of worlds or situations intrigued several logicians. As a solution, Fine gave a two-sorted semantics. We overview the semantics as well as some further work of Fine in the area of relevance logic. Then we show that beyond supplying technical results such as soundness, completeness and the finite model property (fmp) for many logics, the operational–relational semantics provides footing for an informal interpretation and it naturally leads to an interpretation (...) in terms of relevance. (shrink)

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

The decidability of the logic of pure ticket entailment means that the problem of inhabitation of simple types by combinators over the base { B, B′, I, W } is decidable too. Type-assignment systems are often formulated as natural deduction systems. However, our decision procedure for this logic, which we presented in earlier papers, relies on two sequent calculi and it does not yield directly a combinator for a theorem of ${T_\to}$. Here we describe an algorithm to extract an inhabitant (...) from a sequent calculus proof—without translating the proof into another proof system. (shrink)