Pub Date : 2022-06-23DOI: 10.18778/0138-0680.2022.11
Daniela Glavaničová, Tomasz Jarmużek, Mateusz Klonowski, P. Kulicki
In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. we will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly as in Anderson-Kanger's reduction, which uses different intensional implications and constants.
{"title":"Tableaux for some deontic logics with the explicit permission operator","authors":"Daniela Glavaničová, Tomasz Jarmużek, Mateusz Klonowski, P. Kulicki","doi":"10.18778/0138-0680.2022.11","DOIUrl":"https://doi.org/10.18778/0138-0680.2022.11","url":null,"abstract":"In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. we will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly as in Anderson-Kanger's reduction, which uses different intensional implications and constants.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43519163","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 : 2022-06-08DOI: 10.18778/0138-0680.2022.08
Faiz M. Khan, Imran Khan, W. Ahmad
In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate the said method.
{"title":"A Benchmark Similarity Measures for Fermatean Fuzzy Sets","authors":"Faiz M. Khan, Imran Khan, W. Ahmad","doi":"10.18778/0138-0680.2022.08","DOIUrl":"https://doi.org/10.18778/0138-0680.2022.08","url":null,"abstract":"In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate the said method.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49605000","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 : 2022-06-07DOI: 10.18778/0138-0680.2022.06
M. Mishra, A. Sarma
Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. In general, an agent in a state of moral conflict, ought to act on two or more events simultaneously, but fails to do all of them at once. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest's paraconsistent logic LP, and extending our examination to the deontic extension of LP known as DLP. We illustrate our work with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to come up with a significant set of principles to accommodate Arjuna's moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the relationship between the actual world and the context-sensitive ideal world.
{"title":"Tolerating Inconsistencies: A Study of Logic of Moral Conflicts","authors":"M. Mishra, A. Sarma","doi":"10.18778/0138-0680.2022.06","DOIUrl":"https://doi.org/10.18778/0138-0680.2022.06","url":null,"abstract":"Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. In general, an agent in a state of moral conflict, ought to act on two or more events simultaneously, but fails to do all of them at once. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest's paraconsistent logic LP, and extending our examination to the deontic extension of LP known as DLP. We illustrate our work with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to come up with a significant set of principles to accommodate Arjuna's moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the relationship between the actual world and the context-sensitive ideal world.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47363216","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 : 2022-06-07DOI: 10.18778/0138-0680.2022.03
Abolfazl Alam, Morteza Moniri
In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory (rm S_2 ^1(PV)) has bounded model companion then (rm NP=coNP). We also study bounded versions of some other related notions such as Stone topology.
{"title":"Models of Bounded Arithmetic Theories and Some Related Complexity Questions","authors":"Abolfazl Alam, Morteza Moniri","doi":"10.18778/0138-0680.2022.03","DOIUrl":"https://doi.org/10.18778/0138-0680.2022.03","url":null,"abstract":"In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory (rm S_2 ^1(PV)) has bounded model companion then (rm NP=coNP). We also study bounded versions of some other related notions such as Stone topology.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48582241","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 : 2022-01-07DOI: 10.18778/0138-0680.2022.02
T. Braüner
This paper is about non-labelled proof-systems for hybrid logic, that is, proof-systems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that non-labelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.
{"title":"Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts","authors":"T. Braüner","doi":"10.18778/0138-0680.2022.02","DOIUrl":"https://doi.org/10.18778/0138-0680.2022.02","url":null,"abstract":"This paper is about non-labelled proof-systems for hybrid logic, that is, proof-systems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that non-labelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49257569","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 : 2021-11-09DOI: 10.18778/0138-0680.2021.24
A. Belikov, D. Zaitsev
The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius' (and thus, Aristotle's) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.
{"title":"A Variant of Material Connexive Logic","authors":"A. Belikov, D. Zaitsev","doi":"10.18778/0138-0680.2021.24","DOIUrl":"https://doi.org/10.18778/0138-0680.2021.24","url":null,"abstract":"The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius' (and thus, Aristotle's) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41510349","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 : 2021-11-09DOI: 10.18778/0138-0680.2021.26
T. Aravanis
Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.
{"title":"An Epistemological Study of Theory Change","authors":"T. Aravanis","doi":"10.18778/0138-0680.2021.26","DOIUrl":"https://doi.org/10.18778/0138-0680.2021.26","url":null,"abstract":"Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49176934","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 : 2021-11-09DOI: 10.18778/0138-0680.2021.22
Tomoaki Kawano
In this study, new sequent calculi for a minimal quantum logic ((bf MQL)) are discussed that involve an implication. The sequent calculus (bf GO) for (bf MQL) was established by Nishimura, and it is complete with respect to ortho-models (O-models). As (bf GO) does not contain implications, this study adopts the strict implication and constructs two new sequent calculi (mathbf{GOI}_1) and (mathbf{GOI}_2) as the expansions of (bf GO). Both (mathbf{GOI}_1) and (mathbf{GOI}_2) are complete with respect to the O-models. In this study, the completeness and decidability theorems for these new systems are proven. Furthermore, some details pertaining to new rules and the strict implication are discussed.
{"title":"Sequent Calculi for Orthologic with Strict Implication","authors":"Tomoaki Kawano","doi":"10.18778/0138-0680.2021.22","DOIUrl":"https://doi.org/10.18778/0138-0680.2021.22","url":null,"abstract":"In this study, new sequent calculi for a minimal quantum logic ((bf MQL)) are discussed that involve an implication. The sequent calculus (bf GO) for (bf MQL) was established by Nishimura, and it is complete with respect to ortho-models (O-models). As (bf GO) does not contain implications, this study adopts the strict implication and constructs two new sequent calculi (mathbf{GOI}_1) and (mathbf{GOI}_2) as the expansions of (bf GO). Both (mathbf{GOI}_1) and (mathbf{GOI}_2) are complete with respect to the O-models. In this study, the completeness and decidability theorems for these new systems are proven. Furthermore, some details pertaining to new rules and the strict implication are discussed.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44300967","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 : 2021-10-14DOI: 10.18778/0138-0680.2021.21
K. Sasaki
In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system (vdash_{bf Sc}) for classical propositional logic with only structural rules, and prove that (vdash_{bf Sc}) does not allow improper derivations in general. For instance, the sequent (Rightarrow p to q) cannot be derived from the sequent (p Rightarrow q) in (vdash_{bf Sc}). In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of (vdash_{bf Sc}). We also consider whether an improper derivation can be described generally by using (vdash_{bf Sc}).
{"title":"Sequent Systems without Improper Derivations","authors":"K. Sasaki","doi":"10.18778/0138-0680.2021.21","DOIUrl":"https://doi.org/10.18778/0138-0680.2021.21","url":null,"abstract":"In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones.\u0000In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system (vdash_{bf Sc}) for classical propositional logic with only structural rules, and prove that (vdash_{bf Sc}) does not allow improper derivations in general. For instance, the sequent (Rightarrow p to q) cannot be derived from the sequent (p Rightarrow q) in (vdash_{bf Sc}). In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of (vdash_{bf Sc}). We also consider whether an improper derivation can be described generally by using (vdash_{bf Sc}).","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46645935","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 : 2021-09-02DOI: 10.18778/0138-0680.2021.16
Sandra M. López
Six hopefully interesting variants of the logics BN4 and E4 – which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively – were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics.
{"title":"Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B","authors":"Sandra M. López","doi":"10.18778/0138-0680.2021.16","DOIUrl":"https://doi.org/10.18778/0138-0680.2021.16","url":null,"abstract":"Six hopefully interesting variants of the logics BN4 and E4 – which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively – were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46844856","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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