According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions.
The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems in the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.
| Identifer | oai:union.ndltd.org:DITED/urn:dited:bn:29635 |
| Date | January 2005 |
| Creators | Almeida, João Marcos de, 1974- |
| Contributors | Caleiro, Carlos Manuel Costa Lourenço, 1970-, Carnielli, Walter Alexandre |
| Publisher | Instituições portuguesas -- UTL-Universidade Técnica de Lisboa -- IST-Instituto Superior Técnico -- -Departamento de Matemática, Instituições estrangeiras -- Unicamp-Universidade Estadual de Campinas -- IFCH-Instituto de Filosofia e Ciências Humanas -- -Departamento de Filosofia |
| Source Sets | National Library of Portugal DiTeD ETD Repository |
| Language | English |
| Detected Language | English |
| Type | phdthesis |
| Source | Lisboa |
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