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Abstract: An exponential is a unary operator, reminiscent of a modality. We suggest that exponentials be regarded as logic transformers, transforming paraconsistent logics to consistent logics. Consistent logics may appear as certain syntactic subsets of paraconsistent logics. We consider this embedding algebraically and see that an exponential is both a projection and an interior operation. We consider herein a logic constructible duality which is a conservative extension of the paraconsistent version... (Update)
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BibTeX entry: (Update)
@misc{ patterson-exponentials,
author = "Anna Patterson and Tom Costello",
title = "Exponentials as Projections from Paraconsistent Logics",
url = "citeseer.ist.psu.edu/362939.html" }
Citations (may not include all citations):242 Linear logic (context) - Girard - 1987
124 Lattice Theory (context) - Birkhoff - 1948
34 Intuitionism -- An Introduction (context) - Heyting - 1966
31 An algebraic approach to nonclassical logics (context) - Rasiowa - 1974
28 Autonomous categories (context) - Barr - 1979
27 Topological representations of distributive lattices and bro.. (context) - Stone - 1937
24 The algebra of topology (context) - McKinsey - 1944
17 Constructible falsity and inexact predicates (context) - Nelson - 1984
16 On closed elements in closure algebras (context) - McKinsey - 1946
12 the combination of subalgebras (context) - Birkhoff - 1933
6 Intuitionistic logic (context) - Fitting - 1969
2 Bulletin of the Association of Symbolic Logic (context) - Patterson
1 lattices and constructive logic with strong negation (context) - Pest, -- et al. - 1977
1 Constructible falsity (context) - Mathematics, Nelson - 1949
1 Linear Logic through Constructibe Falsity (context) - Patterson
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