A Graph-theoretic Account of Logics

Autor(es)

Sernadas, Amilcar ^{[1, 2]} ; Sernadas, Cristina ^{[1, 2]} ; Rasga, Joao ^{[1, 2]} ; Coniglio, Marcelo ^{[3, 4]}

Afiliação do(s) autor(es)

^[1] Univ Tecn Lisboa, Dept Math, Inst Super Tecn, Lisbon - Portugal

^[2] Inst Telecomunicacoes, SQIG, Lisbon - Portugal

^[3] Univ Estadual Campinas, Dept Philosophy, Campinas - Brazil

^[4] Univ Estadual Campinas, CLE, Campinas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF LOGIC AND COMPUTATION; v. 19, n. 6, p. 1281-1320, DEC 2009.
• Citações Web of Science: 7

Resumo

A graph-theoretic account of logics is explored based on the general notion of in-graph (i.e: a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as multi-graphs (in-graphs). After defining a category freely generated by a in-graph. formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with non-deteministic semantics, and subsume all logics endowed with an algebraic semantics, (AU)

• Processo FAPESP: 04/14107-2 - Logical consequence and combinations of logics: fundaments and efficient applications
• Beneficiário: Walter Alexandre Carnielli
• Modalidade de apoio: Auxílio à Pesquisa - Temático