Modal logic

Paul Gochet
Table of contents

Standard elementary logic studies the deductive inferences which rest on two sets of logical constants: the connectives ‘not’, ‘and’, ‘either … or …’, ‘if … then …’ and the quantifiers ‘all’ and ‘some’. Modal logic extends the logical lexicon in order to account for the validity or non-validity of inferences which depends on the presence of modal terms such as ‘necessarily’ or ‘possibly’. With respect to arguments involving these terms, intuition cannot be trusted. Even the best logicians and philosophers fall prey to fallacies in this area. For instance, Etchemendy (1990: 87) discovered a hidden fallacious move in Tarski’s account of logical consequence, where he went from a statement of the form ‘Necessarily if p and q, then not r’ to a statement of the form ‘if p then necessarily if q then not r’. Anscombe (1959: 138) spotted another unsound move in a famous monograph on epistemology:

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References

Ackrill, J.L.
(ed.) 1963 Aristotle’s Categories and De interpretatione. Oxford University Press.Google Scholar logo with link to Google Scholar
Anscombe, G.E.M.
1959 An introduction to Wittgensteins’s Tractatus. Hutchinson.Google Scholar logo with link to Google Scholar
Aristotle: see Ackrill
(ed.) 1963 and Ross (ed.) 1928..Google Scholar logo with link to Google Scholar
Bailhache, P.
1991 Essai de logique déontique. Vrin.Google Scholar logo with link to Google Scholar
Barcan Marcus, R.
1946 A functional calculus of first order based on strict implication. The Journal of Symbolic Logic 11: 1–17. Google Scholar logo with link to Google Scholar
1993 Modalities. Oxford University Press.Google Scholar logo with link to Google Scholar
Van Benthem, J.
1977 Tense logic and standard logic. Logique et Analyse 80: 395–437.Google Scholar logo with link to Google Scholar
1983a The logic of time. Reidel. Google Scholar logo with link to Google Scholar
1983b Modal logic and classical logic. Bibliopolis.Google Scholar logo with link to Google Scholar
Bressan, A.
1972 A general interpreted modal calculus. Yale University Press.Google Scholar logo with link to Google Scholar
Boolos, G.
1993 The logic of provability. Cambridge University Press.Google Scholar logo with link to Google Scholar
Catach, L.
1991 Tableaux: A general theorem prover for modal logics. Journal of Automated Reasoning 7: 489–510. Google Scholar logo with link to Google Scholar
Chellas, B.
1980 Modal logic. Cambridge University Press. Google Scholar logo with link to Google Scholar
Cresswell, M.J.
1990 Entities and indices. Kluwer. Google Scholar logo with link to Google Scholar
Etchemendy, J.
1990 The concept of logical consequence. Harvard University Press.Google Scholar logo with link to Google Scholar
Feys, R.
1965 Modal logics. Nauwelaerts.Google Scholar logo with link to Google Scholar
Fitting, M.
1983 Proof methods for modal and intuitionistic logics. Reidel. Google Scholar logo with link to Google Scholar
1993 Basic modal logic. In D. Gabbay et al. (eds.) Handbook of logic in artificial intelligence and logic programming: 368–448. Oxford University Press.Google Scholar logo with link to Google Scholar
Gabbay, D.
1976 Investigations in modal and tense logics. Reidel.Google Scholar logo with link to Google Scholar
Gabbay, D. & F. Guenthner
(eds.) 1984 Handbook of philosophical logic. vol. 2. Reidel.  BoPGoogle Scholar logo with link to Google Scholar
Gabbay, D
et al. 1994 Temporal logic. Oxford University Press. Google Scholar logo with link to Google Scholar
Gardies, J-L.
1979 Essai sur la logique des modalités. PUF.Google Scholar logo with link to Google Scholar
Gillet, E. & P. Gochet
1994 A new approach to logical omniscience. Calculemos.Google Scholar logo with link to Google Scholar
Goldblatt, R.
1992 Logics of time and computation. Center for the Study of Language and Information, Stanford.Google Scholar logo with link to Google Scholar
Halpern, J. & Y.O. Moses
1985 A guide to the modal logics of knowledge and belief. IJCAI: 480–490.Google Scholar logo with link to Google Scholar
Hintikka, J.
1962 Knowledge and belief. Cornell University Press.Google Scholar logo with link to Google Scholar
Hughes, G.E. & M.J. Cresswell
1968 An introduction to modal logic. Methuen.Google Scholar logo with link to Google Scholar
Lemmon, E.J.
1977 An introduction to modal logic. Blackwell.Google Scholar logo with link to Google Scholar
Lewis, I. & C.H. Langford
1932 Symbolic logic. Dover.Google Scholar logo with link to Google Scholar
Lyons, J.
1977 Semantics, vol. 2. Cambridge University Press.  BoPGoogle Scholar logo with link to Google Scholar
Mcarthur, R.
1976 Tense logic. Reidel. Google Scholar logo with link to Google Scholar
Mints, G.
1992 A short introduction to modal logic. Center for the Study of Language and Information, Stanford.Google Scholar logo with link to Google Scholar
Moisil, G.
1972 Essai sur les logiques non chrysipiennes. Académie Socialiste de Roumanie.Google Scholar logo with link to Google Scholar
Palmer, F.R.
1979 Modality and the English modals. Longman.  BoPGoogle Scholar logo with link to Google Scholar
Prior, A.
1957 Time and modality. Oxford University Press.Google Scholar logo with link to Google Scholar
1967 Past, present and future. Clarendon. Google Scholar logo with link to Google Scholar
1968a Papers on time and tense. Clarendon.Google Scholar logo with link to Google Scholar
1968b Egocentric logic. Noũs 11: 191–207.Google Scholar logo with link to Google Scholar
Ramsay, A.
1988 Formal methods in artificial intelligence. Cambridge University Press.Google Scholar logo with link to Google Scholar
Rautenberg, W.
1979 Klassische und nichtklassische Aussagenlogik. Braunschweig. Google Scholar logo with link to Google Scholar
Richards, B
et al. 1989 Temporal representation and inference. Academic Press.Google Scholar logo with link to Google Scholar
Rescher, N. & A. Urquhart
1971 Temporal logic. Springer. Google Scholar logo with link to Google Scholar
Ross, W.D.
(ed.) 1928 The works of Aristotle: Analytica Priora. Clarendon.Google Scholar logo with link to Google Scholar
Scott, D.
1971 On engendering an illusion of understanding. Journal of Philosophy 787–807. Google Scholar logo with link to Google Scholar
Turner, R.
1990 Truth and modality for knowledge representation. Pitman.Google Scholar logo with link to Google Scholar
Von Wright, G.H.
1951 An essay in modal logic. North-Holland.Google Scholar logo with link to Google Scholar
1984 Truth, knowledge and modality. Blackwell.Google Scholar logo with link to Google Scholar
 
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