Truth Values and Connectives in Some Non-Classical Logics

Fuzzy Descriptions Logics with Fuzzy Truth Values

Fuzzy Description Logics are a family of logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs are open to be extend with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs with fuzzy truth values, allowing to state sentences su...

Proof search issues in some non-classical logics

This thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investigation into issues in proof search in both these senses for some non-classical logics. Gentzen sys...

Non-classical Metatheory for Non-classical Logics

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical meta-theory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena o...

Connectives in Cumulative Logics

Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson’s [11] early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of Sen’s property α, in the spirit of the author’s [9]. The representation results obtained are surprisingly smooth: in the completeness part the choice fu...

Game theoretical semantics for some non-classical logics

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We als...

Labelled non-classical logics