Connexive Extensions of Regular Conditional Logic
DOI:
https://doi.org/10.12775/LLP.2018.012Słowa kluczowe
conditional logic, connexive logic, conditional obligation, deontic logicAbstrakt
The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is also used to establish independence results. Finally, a deontic interpretation of one of the systems is examined and defended.Bibliografia
Chellas, B.F., “Basic conditional logic”, Journal of Philosophical Logic 4, 2 (1975): 133-153. DOI: 10.1007/BF00693270
Chellas, B.F., Modal Logic, Cambridge University Press, 1980. DOI: 10.1017/CBO9780511621192
Lemmon, E.J., “New foundations for Lewis modal systems”, Journal of Symbolic Logic 22, 2 (1957): 176–186. DOI: 10.2307/2964179
Lewis, D., 1973, Counterfactuals, Oxford University Press.
Lowe, E.J., “A simplification of the logic of conditionals”, Notre Dame Journal of Formal Logic 24, 3 (1983): 357–366. DOI: 10.1305/ndjfl/1093870380
McCall, S., “Connexive implication”, Journal of Symbolic Logic 31, 3 (1966): 415–433. DOI: 10.2307/2270458
Mortensen, C., “Aristotle’s thesis in consistent and inconsistent logics”, Studia Logica 43, 1–2 (1984): 107–116. DOI: 10.1007/BF00935744
Nute, D., Topics in Conditional Logic, D. Reidel Publishing Company, 1980. DOI: 10.1007/978-94-009-8966-5
Pizzi, C., “Boethius’ thesis and conditional logic”, Journal of Philosophical Logic 6, 1 (1977): 283–302. DOI: 10.1007/BF00262063
Pizzi, C., and T. Williamson, “Strong Boethius’ thesis and consequential implication”, Journal of Philosophical Logic 26, 5 (1997): 569–588. DOI: 10.1023/A:1004230028063
Stalnaker, R.C., “A theory of conditionals”, pages 41–55 in W.L. Harper, R. Stalnaker, and G. Pearce (eds.), Ifs, D. Reidel Publishing Company, 1968. DOI: 10.1007/978-94-009-9117-0_2
Unterhuber, M., “Beyond system P – Hilbert-style convergence results for conditional logics with a connexive twist”, IfCoLog Journal of Logics and their Applications 3, 3 (2016): 377–412.
Williamson, T., “Modal logic within counterfactual logic”, pages 81–96 in B. Hale and A. Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology, Oxford University Press, 2010. DOI: 10.1093/acprof:oso/9780199565818.003.0005
von Wright, G.H., “A note on deontic logic and derived obligation”, Mind
, 1 (1956): 507–509. DOI: 10.1093/mind/65.1.507
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Statystyki
Liczba wyświetleń i pobrań: 776
Liczba cytowań: 2
