Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00032
M. Kawaguchi, M. Kondo
We consider some properties of quotient algebras of normal eo-algebras by closed congruences and show that (i) there is a one to one correspondence between the set of all closed filters and the set of all closed congruences, (ii) every normal eo-algebra X is isomorphic to a subdirect product of normal eo-algebras {X/Pa}a∈X, where Pa is a maximal element of closed filters not containing a∈X.
{"title":"On quotient algebras of normal eo-algebras by congruences","authors":"M. Kawaguchi, M. Kondo","doi":"10.1109/ISMVL57333.2023.00032","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00032","url":null,"abstract":"We consider some properties of quotient algebras of normal eo-algebras by closed congruences and show that (i) there is a one to one correspondence between the set of all closed filters and the set of all closed congruences, (ii) every normal eo-algebra X is isomorphic to a subdirect product of normal eo-algebras {X/Pa}a∈X, where Pa is a maximal element of closed filters not containing a∈X.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130749840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00024
R. Stankovic, M. Stankovic, C. Moraga, J. Astola
As in the binary case, ternary bent functions are a very small portion of the set of all ternary functions for a given number of variables. For example, for n = 2, there are 486 ternary bent functions out of 19683 ternary functions, which is 2, 47%, and this number reduces exponentially with the increase of n. However, finding, or alternatively, constructing them is a challenging task. A possible approach is based upon the manipulation of known ternary bent functions to construct other ternary bent functions. In this paper, we define Gibbs permutation matrices derived from the Gibbs derivative with respect to the Vilenkin-Chrestenson transform and propose their usage in constructing bent functions. The method can be extended to p-valued bent functions, where p is a prime larger than 3.
{"title":"Remarks on Gibbs Permutation Matrices for Ternary Bent Functions","authors":"R. Stankovic, M. Stankovic, C. Moraga, J. Astola","doi":"10.1109/ISMVL57333.2023.00024","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00024","url":null,"abstract":"As in the binary case, ternary bent functions are a very small portion of the set of all ternary functions for a given number of variables. For example, for n = 2, there are 486 ternary bent functions out of 19683 ternary functions, which is 2, 47%, and this number reduces exponentially with the increase of n. However, finding, or alternatively, constructing them is a challenging task. A possible approach is based upon the manipulation of known ternary bent functions to construct other ternary bent functions. In this paper, we define Gibbs permutation matrices derived from the Gibbs derivative with respect to the Vilenkin-Chrestenson transform and propose their usage in constructing bent functions. The method can be extended to p-valued bent functions, where p is a prime larger than 3.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125286103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00042
George Opsahl, M. Perkowski
This paper illustrates that Ramon Llull’s Logic Machine is a precursor of contemporary computer applications and systems. Logic Machines search the space of all potential solutions and select those that satisfy all constraints. Examples describe SAT solvers, MAX-SAT, and the famous quantum algorithm of Lov Grover satisfiability which forms the basis of Logic Machines as devices composed of a generator and a verifier.
{"title":"From Ramon Llull To Lov Grover: Towards A Universal Logic Machine","authors":"George Opsahl, M. Perkowski","doi":"10.1109/ISMVL57333.2023.00042","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00042","url":null,"abstract":"This paper illustrates that Ramon Llull’s Logic Machine is a precursor of contemporary computer applications and systems. Logic Machines search the space of all potential solutions and select those that satisfy all constraints. Examples describe SAT solvers, MAX-SAT, and the famous quantum algorithm of Lov Grover satisfiability which forms the basis of Logic Machines as devices composed of a generator and a verifier.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124437018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00034
Mike Behrisch
For several types of maximal clones on finite sets, we construct singleton weak bases consisting of an irredundant relation without fictitious coordinates such that every variable identification of it yields a diagonal relation. Moreover, on the three-element set we provide a complete collection of such weak base relations, one for each maximal clone.
{"title":"Weak bases for maximal clones","authors":"Mike Behrisch","doi":"10.1109/ISMVL57333.2023.00034","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00034","url":null,"abstract":"For several types of maximal clones on finite sets, we construct singleton weak bases consisting of an irredundant relation without fictitious coordinates such that every variable identification of it yields a diagonal relation. Moreover, on the three-element set we provide a complete collection of such weak base relations, one for each maximal clone.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130450768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00041
Shuolin Li, Jordi Coll, Djamal Habet, Chu Min Li, F. Manyà
We define a tableau calculus for solving the Maximum Satisfiability Problem for propositional signed formulas (Signed MaxSAT) and prove its soundness and completeness. We also describe how it can be naturally extended when we distinguish between hard and soft signed formulas.
{"title":"A Tableau Calculus for Signed Maximum Satisfiability","authors":"Shuolin Li, Jordi Coll, Djamal Habet, Chu Min Li, F. Manyà","doi":"10.1109/ISMVL57333.2023.00041","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00041","url":null,"abstract":"We define a tableau calculus for solving the Maximum Satisfiability Problem for propositional signed formulas (Signed MaxSAT) and prove its soundness and completeness. We also describe how it can be naturally extended when we distinguish between hard and soft signed formulas.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131377450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00017
N. Kamide
A Gentzen-style sequent calculus GMA4 is introduced for a modal extension MA4 of Avron’s self-extensional paradefinite four-valued logic. A new Gentzen-style sequent calculus GS4* for normal modal logic S4 is obtained from GMA4 by adding two special inference rules. A theorem for equivalence between GS4* and Kripke’s Gentzen-style sequent calculus GS4 for S4 is proved. Cut- and contraposition-elimination theorems for GMA4 and GS4* are proved. The self-extensional properties of GMA4 and GS4* are obtained from the contraposition-elimination theorems.
{"title":"Self-extensional Paradefinite Four-valued Modal Logic Compatible with Standard Modal Logic","authors":"N. Kamide","doi":"10.1109/ISMVL57333.2023.00017","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00017","url":null,"abstract":"A Gentzen-style sequent calculus GMA4 is introduced for a modal extension MA4 of Avron’s self-extensional paradefinite four-valued logic. A new Gentzen-style sequent calculus GS4* for normal modal logic S4 is obtained from GMA4 by adding two special inference rules. A theorem for equivalence between GS4* and Kripke’s Gentzen-style sequent calculus GS4 for S4 is proved. Cut- and contraposition-elimination theorems for GMA4 and GS4* are proved. The self-extensional properties of GMA4 and GS4* are obtained from the contraposition-elimination theorems.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"465 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123253853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00047
P. Shmerko, S. Yanushkevich, M. Perkowski, Y. Iwashita, A. Stoica
This paper discovers an emerging area of application of the advanced Multivalued Logic (MVL), – a collaboration between humans and autonomous machines in the first responder teams (firefighters, search-and-rescue operators, disaster response personnel, and military special operations forces). We developed an approach to formalization of the collaboration protocols (also known as contagion protocols) that model the human-machine teaming in emergency missions. MVL techniques satisfy the requirements of encoding the states of stress and trust, and their propagation between the teammates. Advanced MVL techniques are also useful for other applications, such as modeling the contagion of infection, or the spread of rumors, ideas, panic, and fear.
{"title":"Discovering Emerging Applications of Multi-Valued Logic: Protocols for Human-Autonomy Teaming","authors":"P. Shmerko, S. Yanushkevich, M. Perkowski, Y. Iwashita, A. Stoica","doi":"10.1109/ISMVL57333.2023.00047","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00047","url":null,"abstract":"This paper discovers an emerging area of application of the advanced Multivalued Logic (MVL), – a collaboration between humans and autonomous machines in the first responder teams (firefighters, search-and-rescue operators, disaster response personnel, and military special operations forces). We developed an approach to formalization of the collaboration protocols (also known as contagion protocols) that model the human-machine teaming in emergency missions. MVL techniques satisfy the requirements of encoding the states of stress and trust, and their propagation between the teammates. Advanced MVL techniques are also useful for other applications, such as modeling the contagion of infection, or the spread of rumors, ideas, panic, and fear.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123935200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1109/ISMVL57333.2023.00012
Kennichi Nakamura, Hiroki Nakahara
Generative adversarial networks (GANs), which can generate and transform data, have been attracting attention. However, the model must be lightweight and fast when applied in the field. As for the ternarization of GAN, (TernaryGAN,) which restricts the value of the weights to {−1, 0, +1} during forwarding propagation of the generator, has already been proposed. In this paper, we investigated by experiment how ternary generator and/or discriminator affects the training of GANs. To make not only generator ternary, but also discriminator, we propose the DGR (Decomposition with Gradient Retained) method, which can change discriminator’s input images to binary. We trained GANs for the cases where the generator and the discriminator are ternarized, and for the case where only one of them is ternarized, and measured the degree of image degradation using the FID (Fréchet inception distance) score. Only the ternarized generator is showed the lowest accuracy degradation, implying that GANs contain some parts that are not suitable for ternarization. We found the useful insight that when reducing the weight of GAN, the generator can be compressed relatively more, while the discriminator should not be so much.
生成式对抗网络(GANs)是一种能够生成和转换数据的网络，一直受到人们的关注。然而，该模型在现场应用时必须是轻量级的和快速的。对于GAN的三化，已经提出了(TernaryGAN)，它将生成器转发传播过程中的权值限制为{−1,0，+1}。本文通过实验研究了三元生成器和/或鉴别器对gan训练的影响。为了实现生成器和鉴别器的三元化，我们提出了将鉴别器的输入图像转换为二值化的DGR (Decomposition with Gradient Retained)方法。我们训练了生成器和鉴别器被三化的情况下的gan，以及只有其中一个被三化的情况下的gan，并使用FID (fr起始距离)分数来测量图像退化的程度。只有三元化生成器的精度下降最小，这表明gan中含有一些不适合三元化的部分。我们发现了一个有用的见解，当减少GAN的重量时，生成器可以被相对地压缩更多，而鉴别器不应该被压缩那么多。
{"title":"A Consideration on Ternary Adversarial Generative Networks","authors":"Kennichi Nakamura, Hiroki Nakahara","doi":"10.1109/ISMVL57333.2023.00012","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00012","url":null,"abstract":"Generative adversarial networks (GANs), which can generate and transform data, have been attracting attention. However, the model must be lightweight and fast when applied in the field. As for the ternarization of GAN, (TernaryGAN,) which restricts the value of the weights to {−1, 0, +1} during forwarding propagation of the generator, has already been proposed. In this paper, we investigated by experiment how ternary generator and/or discriminator affects the training of GANs. To make not only generator ternary, but also discriminator, we propose the DGR (Decomposition with Gradient Retained) method, which can change discriminator’s input images to binary. We trained GANs for the cases where the generator and the discriminator are ternarized, and for the case where only one of them is ternarized, and measured the degree of image degradation using the FID (Fréchet inception distance) score. Only the ternarized generator is showed the lowest accuracy degradation, implying that GANs contain some parts that are not suitable for ternarization. We found the useful insight that when reducing the weight of GAN, the generator can be compressed relatively more, while the discriminator should not be so much.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133104530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1109/ISMVL57333.2023.00031
Igor Sedl'ar
Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular expressions with applications in proving program equivalence. We extend the language of Kleene algebra with tests so that it is sufficient to formalize reasoning about a simplified version weighted programs. We introduce relational semantics for the extended language, and we generalize the relational semantics to an appropriate extension of Kleene algebra with tests, called Kleene algebra with weights and tests. We demonstrate by means of an example that Kleene algebra with weights and tests offers a simple algebraic framework for reasoning about equivalence and optimal runs of weighted programs.
{"title":"Kleene Algebra With Tests for Weighted Programs","authors":"Igor Sedl'ar","doi":"10.1109/ISMVL57333.2023.00031","DOIUrl":"https://doi.org/10.1109/ISMVL57333.2023.00031","url":null,"abstract":"Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular expressions with applications in proving program equivalence. We extend the language of Kleene algebra with tests so that it is sufficient to formalize reasoning about a simplified version weighted programs. We introduce relational semantics for the extended language, and we generalize the relational semantics to an appropriate extension of Kleene algebra with tests, called Kleene algebra with weights and tests. We demonstrate by means of an example that Kleene algebra with weights and tests offers a simple algebraic framework for reasoning about equivalence and optimal runs of weighted programs.","PeriodicalId":419220,"journal":{"name":"2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL)","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131984990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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