{"title":"Infectious and transparent emotivism","authors":"J. J. Joaquin","doi":"10.1080/11663081.2021.2016242","DOIUrl":"https://doi.org/10.1080/11663081.2021.2016242","url":null,"abstract":"Emotivists like Ayer claim that moral sentences are devoid of cognitive meaning since they only evince attitudinal approval or disapproval of actions. In this paper, I explore two non-classical semantic frameworks for such a view. In particular, I look into the semantics for an infectious logic and a transparent logic. Finally, I show how each of these semantic frameworks accounts for the logical behaviour of these meaningless moral sentences and their upshots to moral reasoning; in particular, how each framework addresses (an emotivist variant of) Jörgensen's dilemma.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"14 1","pages":"1 - 10"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87168328","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":"Formal explanations as logical derivations","authors":"Francesco A. Genco","doi":"10.1080/11663081.2021.2010435","DOIUrl":"https://doi.org/10.1080/11663081.2021.2010435","url":null,"abstract":"According to a longstanding philosophical tradition dating back to Aristotle, certain proofs do not only certify the truth of their conclusion but also explain it. Lately, much effort is being devoted to logically characterise the explanatory relation of grounding, especially by proof-theoretical means. Nevertheless, no thorough investigation of the resulting notion of formal explanation exists. We show that formal explanations can be seen as logical derivations of a particular kind and study the interactions between grounding and logical rules, formal explanations and logical derivations. We define a minimal calculus that captures both grounding and logical derivability, and show by a normalisation procedure that grounding rules are proof-theoretically balanced with respect to logical elimination rules. The introduced calculus enables us to combine logical derivations and explanations, to distinguish explanatory parts of derivations from non-explanatory parts, and to compose explanations in order to construct chains of consecutive grounding steps.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"4 1","pages":"279 - 342"},"PeriodicalIF":0.0,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90472905","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":"On the modal interpretation of the connective of realisation","authors":"A. Karczewska","doi":"10.1080/11663081.2021.1982552","DOIUrl":"https://doi.org/10.1080/11663081.2021.1982552","url":null,"abstract":"The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under most accounts it distributes over all Boolean connectives. Nonetheless, there are good reasons to consider weaker kinds of realisation, which lack some distributive laws. Three kinds of semantics for such weak realisation were provided: many-valued, set-theoretic and relational. The paper addresses the problem of Jarmużek's interpretation of the connective of realisation in relational models. It is argued that Jarmużek truth condition for the connective of realisation is tantamount to imposing symmetry on the relation of accessibility in a model. Moreover, a simplified semantics as well as axiom system for Jarmużek system are presented. Finally, a unification with Tkaczyk's – most general -- results is provided by proving completeness result for the axiom system with respect to Tkaczyk-style set-theoretic semantics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"143 1","pages":"221 - 233"},"PeriodicalIF":0.0,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90831301","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":"Non-commutative propositional logic with short-circuit evaluation","authors":"J. Bergstra, A. Ponse, Daan J. C. Staudt","doi":"10.1080/11663081.2021.2010954","DOIUrl":"https://doi.org/10.1080/11663081.2021.2010954","url":null,"abstract":"Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first is insufficient to determine the value of the expression. Compound statements are evaluated from left to right. Short-circuit evaluation is widely used in programming, with negation and sequential conjunction and disjunction as primitives. We study the question of which laws axiomatise short-circuit evaluation. In MSCL (memorising short-circuit logic), atoms (propositional variables) evaluate to true or false, and in the evaluation of a compound statement, the first evaluation result of each atom is memorised. Hence, MSCL is 'Non-commutative propositional logic with short-circuit evaluation' and atomic evaluations cannot cause a side effect. Next, we consider the case that atoms can also evaluate to the truth value 'undefined'. For two- and three-valued MSCL, we present evaluation trees as an intuitive semantics and provide complete independent equational axiomatisations.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"65 1","pages":"234 - 278"},"PeriodicalIF":0.0,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85777355","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":"Substitution inconsistencies in Transparent Intensional Logic","authors":"Miloš Kosterec","doi":"10.1080/11663081.2021.1982553","DOIUrl":"https://doi.org/10.1080/11663081.2021.1982553","url":null,"abstract":"This paper presents several important results for Transparent Intensional Logic (TIL). The conversions that are standardly taken to be valid – namely restricted β-conversion by name and β-reduction by value – are shown to be invalid. The core principle on which their validity is based – the so-called Compensation Principle – is also shown to be invalid. Further, the paper demonstrates the flaws of the proof of the Compensation Principle.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"120 1","pages":"355 - 371"},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76122690","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}
C. Areces, H. V. Ditmarsch, Raul Fervari, Bastien Maubert, François Schwarzentruber
{"title":"Copy and remove as dynamic operators","authors":"C. Areces, H. V. Ditmarsch, Raul Fervari, Bastien Maubert, François Schwarzentruber","doi":"10.1080/11663081.2021.1964327","DOIUrl":"https://doi.org/10.1080/11663081.2021.1964327","url":null,"abstract":"In this article, we present a modal logic that extends the basic modal logic with two dynamic operators: copy ( ), which replicates the current model, labelling each copy with a different propositional symbol and respecting accessibility relations even between distinct copies; and remove ( ), which deletes paths in the model that satisfy certain intermediate conditions. We call the resulting logic . We study its computational complexity, and its relative expressivity with respect to (static) modal logics and , and the dynamic epistemic Action Model Logic, .","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"51 1","pages":"181 - 220"},"PeriodicalIF":0.0,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84474350","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":"Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation","authors":"G. Robles, J. Méndez","doi":"10.1080/11663081.2021.1948285","DOIUrl":"https://doi.org/10.1080/11663081.2021.1948285","url":null,"abstract":"Let MK3 and MK3 be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 (resp., MK3 ) be defined exactly as MK3 (resp., MK3 ), except that the characteristic Łukasiewicz-type negation of Kleene's strong 3-valued matrix is replaced by a ‘Gödel-type’ negation (resp., ‘dual Gödel-type’ negation). The aim of this paper is to axiomatize the logics determined by all natural implicative expansions of MK3 and MK3 . The axiomatic formulations are defined by using a ‘two-valued’ Belnap-Dunn semantics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"2010 1","pages":"130 - 153"},"PeriodicalIF":0.0,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73307350","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":"Measuring inconsistency in some branching time logics","authors":"J. Grant","doi":"10.1080/11663081.2021.1915688","DOIUrl":"https://doi.org/10.1080/11663081.2021.1915688","url":null,"abstract":"Branching time logics have been studied in computer science since the 1980s primarily to model the tree of computations for discrete transition systems. Inconsistency measures for propositional logic have been studied since the early 2000s by AI researchers. This paper introduces inconsistency measures for three branching time logics: ABTL, BBTL, and CBTL. In order to measure inconsistency properly in branching time logics, the semantics differs from the standard semantics using the construction of a canonical tree. ABTL extends propositional logic by three pairs of unary operators: next time, path, and eventually. BBTL adds a pair of binary Until operators that can be applied only to propositional logic formulas. CBTL adds the propositional connectives to BBTL formulas. Propositional logic inconsistency measures are extended to these logics and examples of the computation are given. These measures are shown to satisfy intuitively the concepts involved in the branching time logic operators unlike direct extensions of propositional logic inconsistency measures.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"3 1","pages":"85 - 107"},"PeriodicalIF":0.0,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82923241","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":"Two pretabular linear extensions of relevance logic R","authors":"A. Fallahi","doi":"10.1080/11663081.2021.1915687","DOIUrl":"https://doi.org/10.1080/11663081.2021.1915687","url":null,"abstract":"Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett’s famous super-intuitionistic logic LC and the well-known semi-relevance logic RM (= R-Mingle). In this paper, we investigate Anderson and Belnap’s relevance logic R with the extra axiom: (p → q) ∨ (q → p), which we name LR, and which is (much) weaker than RM, and so is not pretabular. This means that over LR, there may be some pretabular extensions other than RM, two of which this paper presents and with which it provides axiomatizations, characteristic algebras, and Routley-Meyer semantics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"97 1","pages":"154 - 179"},"PeriodicalIF":0.0,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74565760","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 note on the complexity of S4.2","authors":"Aggeliki Chalki, Costas D. Koutras, Yorgos Zikos","doi":"10.1080/11663081.2021.1901560","DOIUrl":"https://doi.org/10.1080/11663081.2021.1901560","url":null,"abstract":"is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical logic, where it has been advocated as the ‘correct’ logic of knowledge; it has also found interesting applications in the temporal logic of relativistic spacetime and the metamathematics of forcing in set theory. The satisfiability problem for is -complete: this is a result established in an AiML 2004 paper of Shapirovsky [(2004). On PSPACE-decidability in transitive modal logic. In R. A. Schmidt, I. Pratt-Hartmann, M. Reynolds, & H. Wansing (Eds.), Advances in modal logic 5 (pp. 269–287). King's College Publications] where the complexity classification of emerges as a consequence of a very general method for constructing decision procedures for transitive modal logics. We provide here a ‘classical’ proof in the standard Halpern-Moses style of Halpern and Moses [(1992). A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54(2), 319–379]. With little extra work, it is shown that the -completeness result extends to , the multimodal version of . We prove that the -completeness characterisation of monomodal persists even if we restrict ourselves to fragments with bounded modal depth, but the problem is -complete when it is restricted to formulae with modal depth at most one. The complexity of satisfiability for the fragment of the language with a finite number of propositional variables (but unbounded modal depth) remains -hard. For a finite language and bounded modal depth, -satisfiability can be checked in linear time.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"7 1","pages":"108 - 129"},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72999056","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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