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Page 3641 of Mathematical Reviews Vol. , Issue 94g
[page]

1994
*
Mathematical Reviews
*

If we identify

*a**theory*with the collection*of*its models, then this Vietoris*topology*induces*a**topology*on the set*of*all*theories*. ...*A*special case*of*Gédel’s second incompleteness theorem (that no sufficiently strong*consistent**theory*can prove its own*consistency*) ...##
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Page 1532 of Mathematical Reviews Vol. , Issue 2002C
[page]

2002
*
Mathematical Reviews
*

The measures used

*in*these proofs are the following: weight*of**a*formula*A*, which depends on the kind*of**logical*connectives*in**A*, and the height*of*derivations which*consist**of*primitive rules. ... 2002¢:03014 van Benthem, who has shown how to provide*a*canonical name for any object*in**propositional*type*theory*. ...##
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Frames and MV-algebras

2005
*
Studia Logica: An International Journal for Symbolic Logic
*

We present

doi:10.1007/s11225-005-4649-5
fatcat:vw2k3kxbdjetbcfm3rxhuqo534
*a*preliminary study*of**a*class*of*MV-algebras which is*a*natural generalization*of*the class*of*"algebras*of*continuous func- ...*In*doing so, we shall more generally consider the way that quantales may be obtained by introducing*propositional*geometric*theories*within non-commutative*logic*, generalising the way that such*theories*...*a*full subcategory*of*the category*of**topological*space objects*in*sh( ) (cf. 7]). 3. ...##
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Page 4253 of Mathematical Reviews Vol. , Issue 85j
[page]

1985
*
Mathematical Reviews
*

*A*

*logic*is said to be

*topologically*definable |resp. p.o.s. ... , (3) probability as

*characterizing*our subjective, personal conviction concerning the taking place

*of*cer- tain events, (4) probability as

*characterizing*

*a*given

*theory*“upon consideration

*of*all available ...

##
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Sheafifying Consistent Histories
[article]

2001
*
arXiv
*
pre-print

Isham's topos-theoretic perspective on the

arXiv:quant-ph/0107037v1
fatcat:o2vby7vjwne7tarxkztwtg6pxm
*logic**of*the*consistent*-histories*theory*is extended*in*two ways. ... First, the presheaves*of**consistent*sets*of*history*propositions**in*the topos proposed by Isham are endowed with*a*Vietoris-type*of**topology*and subsequently they are sheafified with respect to it. ... Special thanks to Chris Isham for bringing to my attention appendix*A**in*[34] where the alternative idea to use trapped sets and*a*Vietoris-type*of**topology*on them, rather than sieves on the base poset ...##
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Borel probabilistic and quantitative logic

2011
*
Science China Information Sciences
*

Thus

doi:10.1007/s11432-011-4268-x
fatcat:h6cjkbkuujcpnoa6wvv2svyefy
*a**theory*which we call probabilistic and quantitative*logic**in*the framework*of*classical*propositional**logic*is established. ... It also proves*a*one-to-one correspondence between deductively closed*theories*and*topologically*closed subsets*of*the space*of*all valuations, and*a*one-to-one correspondence between probabilistic truth ... The basic*theory**of*probability*logic*concerns the probabilities*of*consequences*of**a*specific valid inference, which*consists**of*only finitely many formulas, while the classical*propositional**logic*has ...##
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Topologies for intermediate logics
[article]

2012
*
arXiv
*
pre-print

We investigate the problem

arXiv:1205.2547v1
fatcat:3kh247h725h2fojyr6pfhyo3hm
*of**characterizing*the classes*of*Grothendieck toposes whose internal*logic*satisfies*a*given assertion*in*the*theory**of*Heyting algebras, and introduce natural analogues*of*the ... double negation and De Morgan*topologies*on an elementary topos for*a*wide class*of*intermediate*logics*. ... Boolean subtopos*of*the given topos; similarly, the subtopos*of**a*given elementary topos*consisting**of*its sheaves with respect to the De Morgan*topology*(as introduced*in*[2] ) can be*characterized*...##
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Continuity and geometric logic

2014
*
Journal of Applied Logic
*

This paper is largely

doi:10.1016/j.jal.2013.07.004
fatcat:hn25epegnzdrvpf252l2disf5m
*a*review*of*known results about various aspects*of*geometric*logic*. ... The constructivist constraints*of*geometric*logic*guarantee the continuity*of*maps constructed, and can do so from two different points*of*view: for maps as point transformers and maps as bundles. ... Indeed, point-free approaches to*topology*such as locale*theory*and formal*topology*may be understood as describing the points*of**a*space as the models*of**a**propositional*geometric*theory*. ...##
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Page 6906 of Mathematical Reviews Vol. , Issue 2001J
[page]

2001
*
Mathematical Reviews
*

*A*. da Costa (Sao Paulo) 2001j:03050 03B53 S4D10 S4DI5 Mortensen, Chris (5-ADLD-Q; Adelaide)

*Topological*separation principles and

*logical*

*theories*. (English summary) Festschrift

*in*honor

*of*Newton C. ... This paper similarly dualises intuitionism to

*a*para-

*consistent*

*logic*, but the dual is

*a*different

*logic*, namely closed set

*logic*. ...

##
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Zadeh's influence on mathematics

2011
*
Scientia Iranica. International Journal of Science and Technology
*

The purpose

doi:10.1016/j.scient.2011.04.012
fatcat:dzlf6idqmjc7pampnholvpbo7m
*of*this paper is to present Lotfi Zadeh's influence on mathematics. Mathematics rests on the foundation*of**logic*and set*theory*. L.A. ... Zadeh's seminal paper on fuzzy sets laid the groundwork for fuzzy*logic*and thus the foundation*of*fuzzy mathematics. ... Much*of*the early work*in*fuzzy*topology*was based on its similarity with another branch*of**topology*on*a*lattice -locale*theory*. ...##
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Infinitary domain logic for finitary transition systems
[chapter]

1997
*
Lecture Notes in Computer Science
*

*A*corollary

*of*this result is that the same holds for the

*in*nitary Hennessy-Milner

*logic*. ... As

*a*consequence soundness and completeness

*of*the

*in*nitary

*logic*is obtained for the class

*of*nitary transition systems. ... Acknowledgements: The authors are grateful to Jaco de Bakker, Bart Jacobs, Michael Mislove and Yde Venema for several fruitful discussions on the contents

*of*this paper. ...

##
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Topological interpretations of provability logic
[article]

2012
*
arXiv
*
pre-print

They have observed that the dual modality, corresponding to

arXiv:1210.7317v1
fatcat:3x4kqzfg7jdyheruunf3tpai5q
*consistency**in*the context*of*formal arithmetic, has all the basic properties*of*the*topological*derivative operator acting on*a*scattered space ... We give*a*survey*of*the results on*topological*semantics*of*provability*logic*starting from first contributions by Esakia. ... project STCP-CH-RU "Computational proof*theory*". ...##
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A Logic for Probabilities in Semantics
[chapter]

2002
*
Lecture Notes in Computer Science
*

Via Stone duality, following Abramsky's Domain

doi:10.1007/3-540-45793-3_15
fatcat:j2jzttl65be2vhr4m5zi4c6qy4
*Theory**in**Logical*Form, all known interesting categories*of*domains are embedded as subcategories. ... The category offers*a*promising universe*of*semantic domains*characterized*by*a*very rich structure and good preservation properties*of*standard constructions. ... Acknowledgements The research reported here was started when the first author visited the School*of*Computer Science*of*the University*of*Birmingham*in*the Summer*of*2001, supported by*a*guest professorship ...##
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Preface

2006
*
Theoretical Computer Science
*

This paper considers the so-called reflected

doi:10.1016/j.tcs.2006.03.008
fatcat:ctf7saz42fakvbgxamdh4cajzi
*logic**of*proofs, RLP,*consisting**of*proof assertions t is*a*proof*of*F derivable*in*the*logic**of*proofs LP. ... The Lawson*topology*is*a*refinement*of*the better-known Scott*topology*, so*a*stronger notion*of*computability than the more standard notion*of*Scott computability is obtained. ...##
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A predicate extension of real valued logic

2017
*
Archive for Mathematical Logic
*

Eventually we discuss some

doi:10.1007/s00153-017-0558-3
fatcat:lveeq6milbet3h6y5alz44q2fa
*topological*properties*of*the space*of*types*in*our*logic*. ... We study*a*predicate extension*of*an unbounded real valued*propositional**logic*that has been recently introduced. ... Ours is not*a*by-product*of**a*general*theory*, but is*a*specific result to R-*logic*,*in*the vein*of*those*in*[5, §8] for continuous*logic*. ...
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