82 research outputs found
Relevant Categories and Partial Functions
A relevant category is a symmetric monoidal closed category with a diagonal
natural transformation that satisfies some coherence conditions. Every
cartesian closed category is a relevant category in this sense. The
denomination 'relevant' comes from the connection with relevant logic. It is
shown that the category of sets with partial functions, which is isomorphic to
the category of pointed sets, is a category that is relevant, but not cartesian
closed.Comment: 9 pages, one reference adde
Separating the basic logics of the basic recurrences
This paper shows that, even at the most basic level, the parallel, countable
branching and uncountable branching recurrences of Computability Logic (see
http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles
BCI-Algebras and Related Logics
Kabzinski in [6] first introduced an extension of BCI-logic that is isomorphic to BCI-algebras. Kashima and Komori in [7] gave a Gentzen-style sequent calculus version of this logic as well as another sequent calculus which they proved to be equivalent. They used the second to prove decidability of the word problem for BCI-algebras. The decidability proof relies on cut elimination for the second system, this paper provides a fuller and simpler proof of this. Also supplied is a new decidability proof and proof finding algorithm for their second extension of BCI-logic and so for BCI-algebras
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