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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)  ... 

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.  ... 

Frames and MV-algebras

Lawrence P. Belluce, Antonio Di Nola
2005 Studia Logica: An International Journal for Symbolic Logic  
We present 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.  ... 
doi:10.1007/s11225-005-4649-5 fatcat:vw2k3kxbdjetbcfm3rxhuqo534

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  ... 

Sheafifying Consistent Histories [article]

Ioannis Raptis
2001 arXiv   pre-print
Isham's topos-theoretic perspective on the 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  ... 
arXiv:quant-ph/0107037v1 fatcat:o2vby7vjwne7tarxkztwtg6pxm

Borel probabilistic and quantitative logic

HongJun Zhou, GuoJun Wang
2011 Science China Information Sciences  
Thus 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  ... 
doi:10.1007/s11432-011-4268-x fatcat:h6cjkbkuujcpnoa6wvv2svyefy

Topologies for intermediate logics [article]

Olivia Caramello
2012 arXiv   pre-print
We investigate the problem 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  ... 
arXiv:1205.2547v1 fatcat:3kh247h725h2fojyr6pfhyo3hm

Continuity and geometric logic

Steven Vickers
2014 Journal of Applied Logic  
This paper is largely 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.  ... 
doi:10.1016/j.jal.2013.07.004 fatcat:hn25epegnzdrvpf252l2disf5m

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.  ... 

Zadeh's influence on mathematics

J.N. Mordeson
2011 Scientia Iranica. International Journal of Science and Technology  
The purpose 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.  ... 
doi:10.1016/j.scient.2011.04.012 fatcat:dzlf6idqmjc7pampnholvpbo7m

Infinitary domain logic for finitary transition systems [chapter]

Marcello M. Bonsangue, Joost N. Kok
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.  ... 
doi:10.1007/bfb0014553 fatcat:bmwkg5ofmvc5niog3lowwmzv6e

Topological interpretations of provability logic [article]

Lev Beklemishev, David Gabelaia
2012 arXiv   pre-print
They have observed that the dual modality, corresponding to 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".  ... 
arXiv:1210.7317v1 fatcat:3x4kqzfg7jdyheruunf3tpai5q

A Logic for Probabilities in Semantics [chapter]

M. Andrew Moshier, Achim Jung
2002 Lecture Notes in Computer Science  
Via Stone duality, following Abramsky's Domain 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  ... 
doi:10.1007/3-540-45793-3_15 fatcat:j2jzttl65be2vhr4m5zi4c6qy4


Sergei Artemov, Michael Mislove
2006 Theoretical Computer Science  
This paper considers the so-called reflected 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.  ... 
doi:10.1016/j.tcs.2006.03.008 fatcat:ctf7saz42fakvbgxamdh4cajzi

A predicate extension of real valued logic

Stefano Baratella
2017 Archive for Mathematical Logic  
Eventually we discuss some 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.  ... 
doi:10.1007/s00153-017-0558-3 fatcat:lveeq6milbet3h6y5alz44q2fa
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