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Page 940 of Mathematical Reviews Vol. , Issue 82c
[page]

1982
*
Mathematical Reviews
*

-— 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. ...##
###
Page 1535 of Mathematical Reviews Vol. , Issue 2002C
[page]

2002
*
Mathematical Reviews
*

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. ...##
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Page 2313 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

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. ...##
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Page 10 of Mathematical Reviews Vol. 36, Issue 1
[page]

1968
*
Mathematical Reviews
*

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? ...##
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JSL volume 30 issue 4 Cover and Back matter

1965
*
Journal of Symbolic Logic (JSL)
*

Trial and error predicates and the solution to a problem

doi:10.1017/s0022481200055845
fatcat:bxhbwrkfrrfsdfmdd7lrvqzth4
*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. ...##
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Page 664 of Mathematical Reviews Vol. 33, Issue 4
[page]

1967
*
Mathematical Reviews
*

*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 ...

##
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Mathematical modal logic: A view of its evolution
[chapter]

2006
*
Handbook of the History of Logic
*

It concludes with

doi:10.1016/s1874-5857(06)80027-0
fatcat:dihvhmx5vjhdjndl7x5auvqbki
*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 ✸. ...##
###
Mathematical modal logic: A view of its evolution

2003
*
Journal of Applied Logic
*

It concludes with

doi:10.1016/s1570-8683(03)00008-9
fatcat:zhwzfvdeqjg3rgbkqstbxk5yqq
*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 ✸. ...##
###
Fine's Theorem on First-Order Complete Modal Logics
[article]

2017
*
arXiv
*
pre-print

The ultimate point is that the construction

arXiv:1604.02196v2
fatcat:44hld7smkzduxc3opietn5cfoi
*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*[12]*of*the model theory*of*logics that extend the*system*K4, i.e. their Kripke frames are transitive ...##
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The ancient master argument and some examples of tense logic [Special Issue]
[article]

2016

Prior stays true to the

doi:10.14275/2465-2334/20162.cor
fatcat:mcfofzv6qnbd3pvnn7fskptqa4
*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) . ...##
###
Diodorus Cronus and Hellenistic Philosophy

1977
*
Proceedings of the Cambridge Philological Society
*

*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. ...

##
###
The Ancient Master Argument and Some Examples of Tense Logic

2016
*
Argumenta
*
unpublished

Prior stays true to the

fatcat:aew3jtnixvaodowthh7dz5yxni
*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) . ...##
###
Modal Logics that Bound the Circumference of Transitive Frames
[article]

2019
*
arXiv
*
pre-print

Moreover each

arXiv:1905.11617v2
fatcat:k2tygfovibc6rbbaf67sgamjgi
*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. ...##
###
The Modal Multilogic of Geometry

1998
*
Journal of Applied Non-Classical Logics
*

presentation, the proof

doi:10.1080/11663081.1998.10510945
fatcat:x6h4335q5fdzxpqieeo3nh7pwi
*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. ...##
###
Page 45 of Mathematical Reviews Vol. 14, Issue Index
[page]

*
Mathematical Reviews
*

*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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