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-— 3 291-302; MR _ 80j:03034], offers completeness theorems for nonsimple, stable (quantified) modal logics. Audrey McKinney (Poughkeepsie, N.Y.) White, M. J. 82c:03025 An S5 Diodorean modal system. ... In Sections 1-3 the authors study the B,-algebras, i.e. the algebras corresponding to the n-valued matrix of the n-valued logic of D. A. Boétvar [Mat. Sb. ...
Summary: “Today’s diversity of research topics in modal logic is almost bewildering: modal logic appears as a logic of necessity and possibility; a language for studying provability and expressibility ... Ideas and concepts of modal logic are directly applied to the theory of coalgebras: we give an axiomatization and define canonical coalgebras. That leads to a completeness result. ...
A more interesting possibility would be to use an S4.2-modal algebra instead of an §5-modal algebra for discursive logic as an algebra of events. As was shown by R. ... Earlier the author proposed approaching an algebra of events as the discursive system of S. Jaskowski. ...
Chapter I reviews informal logic of tenses, particularly McTaggart on past-present-future and earlier-later. Chap- ter II reviews the solved problem of formalising Diodorean modality. ... In order to capture more of the spirit of predicate logic, the notion of an J-set is further restricted. An J-algebra is a Boolean algebra A, together with unary operators (a/b), indexed by J? ...
Trial and error predicates and the solution to a problem of Mostowski. An algebraic study of Diodorean modal systems. By R. A. BULL . . 58 On the logic of incomplete answers. By M. J. ... BAUSCH 26 An incorrect theorem. By THEODORE HAILPERIN 27 Limiting recursion. By E. MARK GOLD 28 By HILARY PUTNAM 49 193 Limit ultraproducts. By H. ...doi:10.1017/s0022481200055845 fatcat:bxhbwrkfrrfsdfmdd7lrvqzth4
An algebraic study of Diodorean modal systems. J. Symbolic Logic 30 (1965), 58-64. ... The author considers six systems of deontic logic, which arise if we drop the schema [)A 5 A from various systems of alethic modal logic; in particular, formulations of M (Feys-von Wright), B (the ““Brouwersche ...
Handbook of the History of Logic
It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science. ... This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. ... Over the next few years, algebraic techniques were applied to the study of modal systems, using modal algebras: Boolean algebras with an additional operation 16 Who called it "t". to interpret ✸. ...doi:10.1016/s1874-5857(06)80027-0 fatcat:dihvhmx5vjhdjndl7x5auvqbki
It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science. ... This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. ... Over the next few years, algebraic techniques were applied to the study of modal systems, using modal algebras: Boolean algebras with an additional operation 16 Who called it "t". to interpret ✸. ...doi:10.1016/s1570-8683(03)00008-9 fatcat:zhwzfvdeqjg3rgbkqstbxk5yqq
The ultimate point is that the construction of the canonical frame of a modal algebra does not commute with the ultrapower construction. ... Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. ... copy of the powerset (P(ω), ⊆) of the natural numbers, ordered by inclusion. • An extensive study  of the model theory of logics that extend the system K4, i.e. their Kripke frames are transitive ...arXiv:1604.02196v2 fatcat:44hld7smkzduxc3opietn5cfoi
Prior stays true to the Diodorean philosophical stance even if he uses modern logical tools. The significance of the work by Prior marks the beginning of tense logic. ... The third section expounds an argument by Ohrstrom-Hasle. Danish logicians do not consider additional premises for the Master Argument. ... A strictu sensu algebraic semantics for the Diodorean modal systems was proposed in the memorable study of (Bull 1965) . ...doi:10.14275/2465-2334/20162.cor fatcat:mcfofzv6qnbd3pvnn7fskptqa4
of the modal terms 'possible' and 'necessary'. ... The current version is that Diderot was laughed out of court for his inability to answer an absurd algebraic proof of the existence of God propounded by the Swiss mathematician Euler. ... This article is an expanded version of a paper read to the Cambridge Philological Society on 13th January 1977. ...doi:10.1017/s0068673500003941 fatcat:gwv4vs3sxrgbff35r7odr7u64u
Prior stays true to the Diodorean philosophical stance even if he uses modern logical tools. The significance of the work by Prior marks the beginning of tense logic. ... The third section expounds an argument by Øhrstrøm-Hasle. Danish logicians do not consider additional premises for the Master Argument. ... A strictu sensu algebraic semantics for the Diodorean modal systems was proposed in the memorable study of (Bull 1965) . ...fatcat:aew3jtnixvaodowthh7dz5yxni
Moreover each algebra in the variety is a model of the universal theory of the finite ones, and so is embeddable into an ultraproduct of them. ... The variety of modal algebras validating the n-th logic is shown to be generated by the powerset algebras of the finite frames with cycle length bounded by n. ... Acknowledgement I thank Ian Hodkinson and an anonymous referee for helpful comments and suggestions. ...arXiv:1905.11617v2 fatcat:k2tygfovibc6rbbaf67sgamjgi
presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry. ... A spatial logic is a modal logic of which the models are the mathematical models of space. ... Acknowledgement Special acknowledgement is heartly granted to Dimiter Vakarelov who made several helpful comments for improving the readability of the paper. ...doi:10.1080/11663081.1998.10510945 fatcat:x6h4335q5fdzxpqieeo3nh7pwi
An SS Diodorean modal system. 82¢:03025 On some ascending chains of Brouwerian modal logics. 82g:03031 Wojcicki, Ryszard Entailment semantics for T. 82g:03032 von Wright, Georg Henrik Problems and prospects ... Interval logics with applications to study of tense and aspect in English. 82k:03021 Okabe, Mitsuru An interpretation of Aristotle’s modal syllogism. 82i:03029 Omodeo, Eugenio Giovanni Three existence ...
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