The Logic of Unbalanced Subobjects in a Category with Two Closed Structures

Stout, Lawrence Neff

doi:10.1007/978-94-011-2616-8_4

Cited by 22 publications

(14 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From a modern point of view, this means to compare the category of sets with the category of graphs, the category of tolerance spaces, or however we may call the category of these structures (cf. Stout (1992), Lawvere and Schanuel (1996), Lawvere and Rosebrugh (2002)). …”

Section: Part(s ~S) = Part(s)mentioning

confidence: 99%

On the mereological structure of complex states of affairs

Mormann

2010

Synthese

View full text Add to dashboard Cite

Abstract. The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed.Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of ordinary sets. In general, the mereological systems arising from similarity structures turn out to be not Boolean but Heyting systems. Employing Armstrong's notion of thick particulars, similarity structures are shown to capture the mereological structure of complex "chemical states of affairs" such as "being butane" or "being isobutane", structural universals are not needed.

show abstract

Section: Part(s ~S) = Part(s)mentioning

confidence: 99%

On the mereological structure of complex states of affairs

Mormann

2010

Synthese

View full text Add to dashboard Cite

show abstract

“…A second approach to logic of fuzzy sets is to take the intemal logic of unbalanced subobjects as in [18]. Here the underlying category of types is the Goguen category Set(I) and the category of predicates about a fuzzy set (A, a) is given by the subcategory U(A) of Set(I)/(A, a) consisting of morphisms which are both monic and epic.…”

Section: Proof By Cases Comes Frommentioning

confidence: 99%

“…In the setting of [18] the types would be the whole Goguen category Set(L) and the categories of predicates about a fuzzy set (A, ct) would be the lattice of unbalanced subobjects U(A, ct).…”

mentioning

confidence: 99%

A categorical semantics for fuzzy predicate logic

Stout

2010

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…STOUT [16] showed a way out of this dilemma, and it was shown in [18] that Stout's theory postulates an (£,M)-factorization struc-ture with £ not consisting of epimorphisms. The results of [18] axe generalized in [9] and this paper, with strictly categorical proofs.…”

Section: Introductionmentioning

confidence: 99%