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Possible worlds and many truth values

S. K. Thomason
1978 Studia Logica: An International Journal for Symbolic Logic  
Previous work has established the existence of analogues in certain many-valued modal logics of certain familiar systems of ordinary modal logic.  ...  value from a fixed many-valued truth-functional logic.  ...  Theorem 1. Any formula α of any many-valued modal logic M determines the same class of frames as some formula α * of ordinary modal logic K. The proof of Theorem 1 proceeds as follows.  ... 
doi:10.1007/bf02124804 fatcat:dncyplliwvatbjxjpwvf3akqru

Page 748 of Mathematical Reviews Vol. 58, Issue 2 [page]

1979 Mathematical Reviews  
Skala, Heinz J. 58 #504 On many-valued logics, fuzzy sets, fuzzy logics and their applications. Fuzzy Sets and Systems 1 (1978), no. 2, 129-149.  ...  This paper gives a survey of some aspects of many-valued logics and the theory of fuzzy sets.  ... 

Implementing the meta-theory of deductive systems [chapter]

Frank Pfenning, Ekkehard Rohwedder
1992 Lecture Notes in Computer Science  
We illustrate our technique through several examples, the most extensive of which is an interpretation of classical logic in minimal logic through a continuation-passing-style transformation on proofs.  ...  We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit  ...  In Section 4 we sketch a more comprehensive example, verifying an interpretation of classical logic in minimal logic by way of a continuation-passing-style (CPS) transformation on proofs.  ... 
doi:10.1007/3-540-55602-8_190 fatcat:flv72p7sqzbf5aib4gmcpfelm4

Page 190 of Mathematical Reviews Vol. 38, Issue 2 [page]

1969 Mathematical Reviews  
The paper cites previous work on the subject; some of the results have been anticipated, but many are claimed to be new. H. B. Curry (Amsterdam) Jankov, V.  ...  Say that a system A of functions of k-valued logic (here- after called “system”) is complete under EZ if every function of k-valued logic is computable by a system of switching networks which corresponds  ... 

Page 2729 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
There are infinitely many systems of paraconsistent logic; some of them are motivated by philosophical reasons, others origi- nate from scientific or technological problems, for instance, from robotics  ...  in the literature.” 2004d:03057 03B53 de Moraes, Lafayette (BR-PCSP-Q; Sao Paulo); Abe, Jair Minoro (BR-PAUL-II; Sao Paulo) Some results on JaSkowski’s discursive logic.  ... 

Towards the Formalization of Fractional Calculus in Higher-Order Logic [article]

Umair Siddique, Osman Hasan, Sofiène Tahar
2015 arXiv   pre-print
In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover.  ...  In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering.  ...  Earlier formalization was done in the HOL4 theorem prover with the main focus on fractional operators for real-valued functions and the verification of fractional order electrical components.  ... 
arXiv:1505.02140v1 fatcat:hvyf3xhf2nbh7bj4gijiav7rai

Relating Z and First-Order Logic

Andrew P. Martin
2000 Formal Aspects of Computing  
It discusses some of the issues which must be addressed in creating a proof technology for Z, namely schemas, undefinedness, and what kind of logic to use.  ...  Despite being widely regarded as a gloss on first-order logic and set theory, Z has not been found to be very supportive of proof.  ...  Acknowledgements If I have any insight in this area, it has been gained in discussions with members of the Z Standards panel.  ... 
doi:10.1007/s001650070029 fatcat:hxq6mgf52jf3ziw2wxn44ffxtu

Relating Z and first-order logic [chapter]

Andrew Martin
1999 Lecture Notes in Computer Science  
It discusses some of the issues which must be addressed in creating a proof technology for Z, namely schemas, undefinedness, and what kind of logic to use.  ...  Despite being widely regarded as a gloss on first-order logic and set theory, Z has not been found to be very supportive of proof.  ...  Acknowledgements If I have any insight in this area, it has been gained in discussions with members of the Z Standards panel.  ... 
doi:10.1007/3-540-48118-4_17 fatcat:bvidc45le5hubehrv3ltxwxgva

Stabilization of Periodic Switched k-Valued Logical Networks

Yan Gao, Chenchen Liu, Jiaqi Wang
2021 IEEE Access  
PRELIMINARIES This section gives some necessary preliminaries on Cheng product and periodic switched k-valued logical networks, which will be used in the following. A.  ...  In Section II, we recall some preliminaries on Cheng product and problem formulation which will be used in later sections.  ...  The methods, proposed in this paper, are based on k-valued logical networks, which is a generalization of traditional BNs.  ... 
doi:10.1109/access.2021.3077387 fatcat:eeftrrlg4bc5jjiqgxkllovnwa

Paraconsistentization and many-valued logics [article]

Edelcio G. de Souza, Alexandre Costa-Leite, Diogo H. B. Dias
2020 arXiv   pre-print
This paper shows how to transform explosive many-valued systems into paraconsistent logics.  ...  We investigate especially the case of three-valued systems showing how paraconsistent three-valued logics can be obtained from them.  ...  Standard notions and results on many-valued logics can be found in [13] , [17] , [11] , [3] and [19] .  ... 
arXiv:2004.14881v1 fatcat:rjsi74tcqbelbhl53z3iupsfne

Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light [chapter]

Syeda Hira Taqdees, Osman Hasan
2013 Lecture Notes in Computer Science  
Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems.  ...  In particular, we use integral, differential, transcendental and topological theories of multivariable calculus to formally define Laplace transform in higher-order logic and reason about the correctness  ...  verifying many challenging mathematical theorems.  ... 
doi:10.1007/978-3-642-45221-5_50 fatcat:fks2jihksrfalktlbopv5weapy

Quantum view on contextual logic of composite intelligent devices [article]

E. D. Vol
2013 arXiv   pre-print
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate  ...  In this preliminary communication we consider only the simplest example of such systems, namely, four- valued probabilistic logical device composed of two logical subsystems.  ...  transformations, namely one can prove that the following theorem has place.Theorem 2 : let A is DP in composite system and G some one-place admissible transformation.Then A = GAG T is decomposable proposition  ... 
arXiv:1301.5419v1 fatcat:fyqol4uukngpvpopa6up4iypua

Page 5172 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
for many-valued logics.  ...  In this framework, we prove the categorical equivalence between different kinds of structures that have been introduced in order to characterize some many- valued logics semantically.  ... 

On Some Universal Propositional Proof Systems for Many-Valued Logic

Artur Khamisyan
2020 Mathematical Problems of Computer Science  
Some uniform Hilbert-like propositional proof system is suggested for all versions of many-valued logic to apply them to 3 versions of 3-valued logic, two of which have only one designated value, and the  ...  last one has two designated values  ...  Acknowledgements This work was supported by the RA MES State Committee of Science, in the frames of the research project № 18T-1B034.  ... 
doi:10.51408/1963-0049 fatcat:m5ggpqfnszh2xm42h24xiwwlbu

The separable axiomatization of the intermediate propositional systems $S_n $ of Gödel

Tsutomu Hosoi
1966 Proceedings of the Japan Academy  
And in our paper 6 we introduced two kinds of axiomatization for these S. But the separation theorem mentioned below does not hold on those axiomatized systems. Separation Theorem.  ...  In [3 GSdel introduced a series of many-valued propositional systems S, which is widely known and is quite frequently made use of when propositional systems are treated.  ...  And we proved in [4 and [5 that the separation theorem holds on LI+ Z. In [6 is proved the Lemma 2.. S LI+Z+X++ Y LI+R.  ... 
doi:10.3792/pja/1195521794 fatcat:ozwblmtnmjamninrs5oywfp4mi
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