Four-valued semantics for relevant logics (and some of their rivals)
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This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the ‘Australian Plan’ semantics, which uses a unary operator ‘⋆’ for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a semantics for the contraction-free relevant logicC (orRW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof.
KeywordsFormal System Unary Operator Completeness Proof Relevant Logic Australian Plan
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- Belnap, N. D., Jr. (1977), ‘A Useful Four-Valued Logic,’ in J.M Dunn and G. Epstein (eds),Modern Uses of Multiple-Valued Logic, Dordrecht, 8–37.Google Scholar
- Belnap, N. D., Jr. (1977), ‘How a Computer Should Think,’ in G. Ryle (ed.),Contemporary Aspects of Philosophy, Oriel Press, 30–55.Google Scholar
- Dunn, J. M. (1976), ‘Intuitive Semantics for First-Degree Entailment and ‘Coupled Trees’,’Philosophical Studies 29, 149–168.Google Scholar
- Priest, G. (1979), ‘Logic of Paradox’,Journal of Philosophical Logic 8, 219–241.Google Scholar
- Priest, G. and R. Sylvan (1992), ‘Simplified Semantics for Basic Relevant Logics’,Journal of Philosophical Logic 21, 217–232.Google Scholar
- Restall, G. (1993), ‘Simplified Semantics for Relevant Logics (and Some of Their Rivals)’,Journal of Philosophical Logic 22, 481–511.Google Scholar
- Routley, R., V. Plumwood, R. Meyer and R. Brady (1982),Relevant Logics and their Rivals, Ridgeview.Google Scholar
- Slaney, J. (1990), ‘A General Logic’,Australian Journal of Philosophy 68, 74–88.Google Scholar
- Slaney, J. (1989), ‘Finite Models for some Non-Classical Logics’, Technical Report TR-ARP-2/90, Automated Reasoning Project, Australian National University, Canberra.Google Scholar