In this commentary I build on Phil Barnard’s distinction of implicational and propositional meanings as an incentive to explore possibilities for bridging the two types of meanings. I argue that, contrary to the claim that musical experiences are ineffable, the subtle implicational meanings that make up the experiential richness of musical qualia may be amenable to linguistic description and ob...

A class of challenge problems derived from a first-order encoding of the implicational propositional calculus is presented.

In this paper, the differently implicational universal triple I inference algorithms of fuzzy reasoning are discussed. We generalize fuzzy reasoning triple I algorithms to differently implicational (1, 2, 1) type universal triple I algorithms, and their solutions (FMP universal triple I solution and FMT universal triple I solution) are structured. As the corollaries of the main results in this ...

In this article we present a class of formulas φn, n ∈ Nat, that need at least 2 assumptions to be proved in a normal proof in Natural Deduction for purely implicational minimal propositional logic. In purely implicational classical propositional logic, with Peirce’s rule, each φn is proved with only one assumption in Natural Deduction in a normal proof. Hence, the formulas φn have exponentiall...

Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective w.r.t. that epimorphism. G. Roçu formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a finitary one (for epimorphisms with finitely presentable domains and codomains). In categories Alg Σ of al...