Mauricio Osorio, A. F. Orellano, Miguel Pérez-Gaspar
{"title":"A family of genuine and non-algebraisable C-systems","authors":"Mauricio Osorio, A. F. Orellano, Miguel Pérez-Gaspar","doi":"10.1080/11663081.2021.1885167","DOIUrl":"https://doi.org/10.1080/11663081.2021.1885167","url":null,"abstract":"ABSTRACT In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsistent logic in terms of three connectives , , and . In this paper, we show that is an axiomatic extension of through the introduction of a non-primitive deductive implication. Furthermore, we prove that is an algebraisable logic with Blok-Pigozzi's method. From the proof that is non-algebraisable logic, we are able to see that is not algebraisable logic and studying the borders of algebrisabilty, we can give an enumerable family of new genuine, paraconsistent and non-algebraisable logics, extensions of . Finally, we introduced n-valued ( ) and infinite-valued logic and show that they are genuine and non-algebraisable paraconsistent ones; in addition, we present semantics for this extensions of by means of Fidel's structures.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"5 1","pages":"56 - 84"},"PeriodicalIF":0.0,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84793614","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}
{"title":"Grounding rules for (relevant) implication","authors":"F. Poggiolesi","doi":"10.1080/11663081.2020.1850048","DOIUrl":"https://doi.org/10.1080/11663081.2020.1850048","url":null,"abstract":"In Poggiolesi [(2020a). Grounding principles for (relevant) implication. Synthese, 1–28], a definition of the notion of grounding in the background of a relevant framework has been introduced; this definition generates some intuitively acceptable grounding principles for relevant implication. In the present paper, our aim is to construct a logic based on that definition. Our logic will be a calculus of natural deduction and will formalise the relation of grounding both as a meta-linguistic relation and as a connective. The calculus will contain grounding rules for relevant implication and will be proved to be sound and complete with respect to the original definition. Finally we will prove the deduction theorem at the grounding level.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"96 1","pages":"26 - 55"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89390781","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}
{"title":"Epistemic space of degradation processes","authors":"Liu Yang, A. Rauzy","doi":"10.1080/11663081.2020.1850047","DOIUrl":"https://doi.org/10.1080/11663081.2020.1850047","url":null,"abstract":"In this article, we present a new approach of modelling epistemic uncertainties in degradation processes. This approach is established in the framework of finite degradation structures (FDSs), which is recently proposed by the authors and can be seen as a formal extension of the fault tree analysis into multistate systems. When epistemic uncertainties are added to the states of the system, it implicitly increases the number of states and make even the Boolean systems become multistate. In the existing approaches, the addition of epistemically uncertain states as well as the new valuation mappings of the operations for those states should be done manually by the analysts depending on the type of system and its components. This manual addition may be time-consuming, error-prone and lack of generality, especially when systems get large and complex. Instead of manually remodelling the system, we propose in this article to automatic transform the model built on FDSs into epistemic space to take into account epistemic uncertainties. The proposed automatic transformations are mathematically defined and explained. As results, the uncertainty-embedded (critical) scenarios and probabilistic indicators like the belief and the plausibility in the Dempter–Shafer theory can be obtained. Illustrative examples with experimental results are also provided.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"35 1","pages":"1 - 25"},"PeriodicalIF":0.0,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72591792","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}
{"title":"Logics of variable inclusion and the lattice of consequence relations","authors":"M. Pra Baldi","doi":"10.1080/11663081.2020.1835330","DOIUrl":"https://doi.org/10.1080/11663081.2020.1835330","url":null,"abstract":"In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic with a composition term. Then, we investigate their position into the lattice of consequence relations over the language of .","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"4 1","pages":"367 - 381"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74606066","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}
{"title":"A basic quasi-Boolean logic of intuitionistic character","authors":"G. Robles","doi":"10.1080/11663081.2020.1826155","DOIUrl":"https://doi.org/10.1080/11663081.2020.1826155","url":null,"abstract":"The logic B is Sylvan and Plumwood's minimal De Morgan logic. The aim of this paper is to investigate extensions of B endowed with a quasi-Boolean negation of intuitionistic character included in 3-valued logic G3 and/or 3-valued logic S5 . Unreduced Routley-Meyer ternary relational semantics are provided for all the logics defined in the paper.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"91 1","pages":"291 - 311"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77293619","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}
{"title":"Metainferential duality","authors":"B. Ré, F. Pailos, D. Szmuc, Paula Teijeiro","doi":"10.1080/11663081.2020.1826156","DOIUrl":"https://doi.org/10.1080/11663081.2020.1826156","url":null,"abstract":"The aim of this article is to discuss the extent to which certain substructural logics are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collections of inferences, and thus substructural logics can be regarded as logics that have fewer valid metainferences that Classical Logic. In order to investigate duality in substructural logics, we will focus on the case study of the logics and , the former lacking Cut, the latter Reflexivity. The sense in which these logics, and metainferences, are dual has yet to be explained in the context of a thorough exposition of duality for frameworks of this sort. Thus, we try to elucidate whether this way of talking holds some ground – specially generalizing one notion of duality available in the specialized literature, the so-called notion of negation duality. In doing so, we hope to shed light on the phenomenon of duality in substructural logics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"74 1","pages":"312 - 334"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87085495","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}
{"title":"Algebraic semantics for propositional superposition logic","authors":"A. Tzouvaras","doi":"10.1080/11663081.2020.1826157","DOIUrl":"https://doi.org/10.1080/11663081.2020.1826157","url":null,"abstract":"We provide a new semantics and a slightly different formalisation for the propositional logic with superposition (PLS) introduced and studied in Tzouvaras [(2018). Propositional superposition logic. Logic Journal of the IGPL, 26(1), 149–190]. PLS results from Propositional Logic (PL) by adding a new binary connective construed as the ‘superposition operation’ and a few axioms about it. The original semantics used in the above paper was the so-called sentence choice semantics (SCS), based on choice functions for all pairs of classical formulas of PL. In contrast, the algebraic or Boolean-value choice semantics (BCS) developed in this paper is based on choice functions for pairs of elements of a Boolean algebra in which the classical sentences take truth values. The Boolean-value choice functions can be subject to similar constraints as those imposed on sentence choice functions. The new axiomatisation is based on the same set of axioms as the previous one but uses a new inference rule, called Rule of Analogy (RA), in place of the rule Salva Veritate (SV) of the previous systems. The Deduction Theorem fails in the systems containing the new rule. As a consequence the completeness theorems for them hold conditionally again, namely the systems are complete with respect to BCS if and only if every consistent set of sentences is extended to a consistent and complete set. Finally connections are established between tautologies of the semantics SCS and those of BCS.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"10 1","pages":"335 - 366"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90783717","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}
{"title":"A logic of negative trust","authors":"G. Primiero","doi":"10.1080/11663081.2020.1789404","DOIUrl":"https://doi.org/10.1080/11663081.2020.1789404","url":null,"abstract":"We present a logic to model the behaviour of an agent trusting or not trusting messages sent by another agent. The logic formalises trust as a consistency checking function with respect to currently available information. Negative trust is modelled in two forms: distrust, as the rejection of incoming inconsistent information; mistrust, as revision of previously held information becoming undesirable in view of new incoming inconsistent information, which the agent wishes to accept. We provide a natural deduction calculus, a relational semantics and prove soundness and completeness results. We overview a number of applications which have been investigated for the proof-theoretical formulation of the logic.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"15 1","pages":"193 - 222"},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75115768","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}
{"title":"Structural proof theory for first-order weak Kleene logics","authors":"Andreas Fjellstad","doi":"10.1080/11663081.2020.1782593","DOIUrl":"https://doi.org/10.1080/11663081.2020.1782593","url":null,"abstract":"Abstract This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"127 1","pages":"272 - 289"},"PeriodicalIF":0.0,"publicationDate":"2020-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75812746","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}
{"title":"Most-intersection of countable sets","authors":"A. Cevik, Selçuk Topal","doi":"10.1080/11663081.2021.1998742","DOIUrl":"https://doi.org/10.1080/11663081.2021.1998742","url":null,"abstract":"We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly infinite) collection of systems. The new operator determines, based on the natural density, the elements which are in ‘most’ sets in a given collection. This notion allows one to define a majority set-membership characteristic of an infinite/finite collection with minimal information loss, compared to the standard intersection operator, when used in statistical ensembles. We also give some applications of the most-intersection operator in formal language theory and hypergraphs. The introduction of the most-intersection operator leads to a large number of applications in pure and applied mathematics some of which we leave open for further study.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"32 1","pages":"343 - 354"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88291076","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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