In the paper (Brauner, 2014) we were concerned with logical formalizations of the reasoning involved in giving correct responses to the psychological tests called the Sally-Anne test and the Smarties test, which test children’s ability to ascribe false beliefs to others. A key feature of the formal proofs given in that paper is that they explicitly formalize the perspective shift to another person that is required for figuring out the correct answers – you have to put yourself in another person’s shoes, so to speak, to give the correct answer. We shall in the present paper be concerned with what happens when answers are given that are not correct. The typical incorrect answers indicate that children failing false-belief tests have problems shifting to a perspective different from their own, to be more precise, they simply reason from their own perspective. Based on this hypothesis, we in the present paper give logical formalizations that in a systematic way model the typical incorrect answers. The remarkable fact that the incorrect answers can be derived using logically correct rules indicates that the origin of the mistakes does not lie in the children’s logical reasoning, but rather in a wrong interpretation of the task.
{"title":"Incorrect Responses in First-Order False-Belief Tests: A Hybrid-Logical Formalization","authors":"T. Braüner","doi":"10.12775/LLP.2020.003","DOIUrl":"https://doi.org/10.12775/LLP.2020.003","url":null,"abstract":"In the paper (Brauner, 2014) we were concerned with logical formalizations of the reasoning involved in giving correct responses to the psychological tests called the Sally-Anne test and the Smarties test, which test children’s ability to ascribe false beliefs to others. A key feature of the formal proofs given in that paper is that they explicitly formalize the perspective shift to another person that is required for figuring out the correct answers – you have to put yourself in another person’s shoes, so to speak, to give the correct answer. We shall in the present paper be concerned with what happens when answers are given that are not correct. The typical incorrect answers indicate that children failing false-belief tests have problems shifting to a perspective different from their own, to be more precise, they simply reason from their own perspective. Based on this hypothesis, we in the present paper give logical formalizations that in a systematic way model the typical incorrect answers. The remarkable fact that the incorrect answers can be derived using logically correct rules indicates that the origin of the mistakes does not lie in the children’s logical reasoning, but rather in a wrong interpretation of the task.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"29 1","pages":"415-445"},"PeriodicalIF":0.5,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47196962","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}
Given the frequency of human error, it seems rational to believe that some of our own rational beliefs are false. This is the axiom of epistemic modesty. Unfortunately, using standard propositional quantification, and the usual relational semantics, this axiom is semantically inconsistent with a common logic for rational belief, namely KD45. Here we explore two alternative semantics for KD45 and the axiom of epistemic modesty. The first uses the usual relational semantics and bisimulation quantifiers. The second uses a topological semantics and standard propositional quantification. We show the two different semantics validate many of the same formulas, though we do not know whether they validate exactly the same formulas. Along the way we address various philosophical concerns.
{"title":"Some Formal Semantics for Epistemic Modesty","authors":"Christopher Steinsvold","doi":"10.12775/llp.2020.002","DOIUrl":"https://doi.org/10.12775/llp.2020.002","url":null,"abstract":"Given the frequency of human error, it seems rational to believe that some of our own rational beliefs are false. This is the axiom of epistemic modesty. Unfortunately, using standard propositional quantification, and the usual relational semantics, this axiom is semantically inconsistent with a common logic for rational belief, namely KD45. Here we explore two alternative semantics for KD45 and the axiom of epistemic modesty. The first uses the usual relational semantics and bisimulation quantifiers. The second uses a topological semantics and standard propositional quantification. We show the two different semantics validate many of the same formulas, though we do not know whether they validate exactly the same formulas. Along the way we address various philosophical concerns.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"29 1","pages":"381-413"},"PeriodicalIF":0.5,"publicationDate":"2020-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48672963","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}
Kulicki and Trypuz (2016) introduced three systems of multi-valued deontic action logic to handle normative conflicts. The first system suggests a pessimistic view on normative conflicts, according to which any conflicting option represents something forbidden; the second system suggests an optimistic view, according to which any conflicting option represents something obligatory; finally, the third system suggests a neutral view, according to which any conflicting option represents something that is neither obligatory nor forbidden. The aim of the present paper is to propose a fourth system in this family, which comes with a realistic view on normative conflicts: a normative conflict remains unsolved unless it is generated by two or more normative sources that can be compared. In accordance with this, we will provide a more refined formal framework for the family of systems at issue, which allows for explicit reference to sources of norms. Conflict resolution is thus a consequence of a codified hierarchy of normative sources.
{"title":"A Realistic View on Normative Conflicts","authors":"Daniela Glavaničová, Matteo Pascucci","doi":"10.12775/llp.2020.001","DOIUrl":"https://doi.org/10.12775/llp.2020.001","url":null,"abstract":"Kulicki and Trypuz (2016) introduced three systems of multi-valued deontic action logic to handle normative conflicts. The first system suggests a pessimistic view on normative conflicts, according to which any conflicting option represents something forbidden; the second system suggests an optimistic view, according to which any conflicting option represents something obligatory; finally, the third system suggests a neutral view, according to which any conflicting option represents something that is neither obligatory nor forbidden. The aim of the present paper is to propose a fourth system in this family, which comes with a realistic view on normative conflicts: a normative conflict remains unsolved unless it is generated by two or more normative sources that can be compared. In accordance with this, we will provide a more refined formal framework for the family of systems at issue, which allows for explicit reference to sources of norms. Conflict resolution is thus a consequence of a codified hierarchy of normative sources.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"29 1","pages":"447-462"},"PeriodicalIF":0.5,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46428342","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}
In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB 1 , is an extension of systems PI, C min and B 1 , and a proper subsystem of Sette’s calculus P 1 . We also investigate the generalization of CB 1 to the hierarchy of related calculi.
{"title":"On the system CB1 and a lattice of the paraconsistent calculi","authors":"J. Ciuciura","doi":"10.12775/llp.2019.035","DOIUrl":"https://doi.org/10.12775/llp.2019.035","url":null,"abstract":"In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB 1 , is an extension of systems PI, C min and B 1 , and a proper subsystem of Sette’s calculus P 1 . We also investigate the generalization of CB 1 to the hierarchy of related calculi.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43803224","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}
Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopv{e}nka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, L"{o}we and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by L"{o}we and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing L"{o}we and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF).
{"title":"Twist-Valued Models for Three-Valued Paraconsistent Set Theory","authors":"W. Carnielli, M. Coniglio","doi":"10.12775/llp.2020.015","DOIUrl":"https://doi.org/10.12775/llp.2020.015","url":null,"abstract":"Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopv{e}nka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, L\"{o}we and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by L\"{o}we and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing L\"{o}we and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF).","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44895209","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}
We present a study of unpublished fragments of Jan F. Drewnowski’s manuscript from the years 1922–1928, which contains his own axiomatics for mereology. The sources are transcribed and two versions of mereology are reconstructed from them. The first one is given by Drewnowski. The second comes from Leśniewski and was known to Drewnowski from Leśniewski’s lectures. Drewnowski’s version is expressed in the language of ontology enriched with the primitive concept of a (proper) part, and its key axiom expresses the so-called weak super-supplementation principle, which was named by Drewnowski “the postulate of the existence of subtractions”. Leśniewski’s axiomatics with the primitive concept of an ingrediens contains the axiom expressing the strong super-supplementation principle. In both systems the collective class of objects from the range of a given non-empty concept is defined as the upper bound of that range. From a historical point of view it is interesting to notice that the presented version of Leśniewski’s axiomatics has not been published yet. The same applies to Drewnowski’s approach. We reconstruct the proof of the equivalence of these two systems. Finally, we discuss questions stemming from their equivalence in frame of elementary mereology formulated in a modern way.
我们提出了一个研究未发表的片段的Jan F. Drewnowski的手稿从年1922-1928，其中包含了他自己的光学公理。来源转录和两个版本的气象学重建从他们。第一个是Drewnowski给出的。第二个来自Leśniewski，德鲁诺夫斯基是在Leśniewski的讲座中知道的。Drewnowski的版本是用本体语言表达的，丰富了一个(固有)部分的原始概念，其关键公理表达了所谓的弱超补原理，被Drewnowski命名为“减法存在性公设”。Leśniewski的公理与一个成分的原始概念包含公理表达强超补充原则。在这两个系统中，来自给定非空概念范围的对象的集合类被定义为该范围的上界。从历史的角度来看，有趣的是，目前提出的Leśniewski的公理化版本还没有发表。这同样适用于Drewnowski的方法。我们重新构造了这两个系统的等价性证明。最后，我们讨论了它们在以现代方式表述的初等气象学框架中的等价性所产生的问题。
{"title":"Mereology with super-supplemention axioms. A reconstruction of the unpublished manuscript of Jan F. Drewnowski","authors":"K. Świętorzecka, Marcin Łyczak","doi":"10.12775/llp.2019.034","DOIUrl":"https://doi.org/10.12775/llp.2019.034","url":null,"abstract":"We present a study of unpublished fragments of Jan F. Drewnowski’s manuscript from the years 1922–1928, which contains his own axiomatics for mereology. The sources are transcribed and two versions of mereology are reconstructed from them. The first one is given by Drewnowski. The second comes from Leśniewski and was known to Drewnowski from Leśniewski’s lectures. Drewnowski’s version is expressed in the language of ontology enriched with the primitive concept of a (proper) part, and its key axiom expresses the so-called weak super-supplementation principle, which was named by Drewnowski “the postulate of the existence of subtractions”. Leśniewski’s axiomatics with the primitive concept of an ingrediens contains the axiom expressing the strong super-supplementation principle. In both systems the collective class of objects from the range of a given non-empty concept is defined as the upper bound of that range. From a historical point of view it is interesting to notice that the presented version of Leśniewski’s axiomatics has not been published yet. The same applies to Drewnowski’s approach. We reconstruct the proof of the equivalence of these two systems. Finally, we discuss questions stemming from their equivalence in frame of elementary mereology formulated in a modern way.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47306675","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}
We present a formal reconstruction of the theories of the medieval logician Robert Kilwardby, focusing on his account of accidental and natural inferences and the underlying modal logic that gives rise to it. We show how Kilwardby’s use of an essentialist modality underpins his connexive account of implication.
{"title":"Per Se Modality and Natural Implication – an Account of Connexive Logic in Robert Kilwardby","authors":"S. Johnston","doi":"10.12775/llp.2019.033","DOIUrl":"https://doi.org/10.12775/llp.2019.033","url":null,"abstract":"We present a formal reconstruction of the theories of the medieval logician Robert Kilwardby, focusing on his account of accidental and natural inferences and the underlying modal logic that gives rise to it. We show how Kilwardby’s use of an essentialist modality underpins his connexive account of implication.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41838626","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}
In this paper, we strengthen Hardy’s [1995] and Ketland’s [2005] arguments on the issues surrounding the self-referential nature of Yablo’s paradox [1993]. We first begin by observing that Priest’s [1997] construction of the binary satisfaction relation in revealing a fixed point relies on impredicative definitions. We then show that Yablo’s paradox is ‘ω-circular’, based on ω-inconsistent theories, by arguing that the paradox is not self-referential in the classical sense but rather admits circularity at the least transfinite countable ordinal. Hence, we both strengthen arguments for the ω-inconsistency of Yablo’s paradox and present a compromise solution of the problem emerged from Yablo’s and Priest’s conflicting theses.
{"title":"ω-circularity of Yablo's paradox","authors":"A. Cevik","doi":"10.12775/llp.2019.032","DOIUrl":"https://doi.org/10.12775/llp.2019.032","url":null,"abstract":"In this paper, we strengthen Hardy’s [1995] and Ketland’s [2005] arguments on the issues surrounding the self-referential nature of Yablo’s paradox [1993]. We first begin by observing that Priest’s [1997] construction of the binary satisfaction relation in revealing a fixed point relies on impredicative definitions. We then show that Yablo’s paradox is ‘ω-circular’, based on ω-inconsistent theories, by arguing that the paradox is not self-referential in the classical sense but rather admits circularity at the least transfinite countable ordinal. Hence, we both strengthen arguments for the ω-inconsistency of Yablo’s paradox and present a compromise solution of the problem emerged from Yablo’s and Priest’s conflicting theses.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44536837","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}
In this paper, we present a logic MML S5 n which is a combination of multilattice logic and modal logic S5. MML S5 n is an extension of Kamide and Shramko’s modal multilattice logic which is a multilattice analogue of S4. We present a cut-free hypersequent calculus for MML S5 n in the spirit of Restall’s one for S5 and develop a Kripke semantics for MML S5 n , following Kamide and Shramko’s approach. Moreover, we prove theorems for embedding MML S5 n into S5 and vice versa. As a result, we obtain completeness, cut elimination, decidability, and interpolation theorems for MML S5 n . Besides, we show the duality principle for MML S5 n . Additionally, we introduce a modification of Kamide and Shramko’s sequent calculus for their multilattice version of S4 which (in contrast to Kamide and Shramko’s original one) proves the interdefinability of necessity and possibility operators. Last, but not least, we present Hilbert-style calculi for all the logics in question as well as for a larger class of modal multilattice logics.
{"title":"On a multilattice analogue of a hypersequent S5 calculus","authors":"Oleg M. Grigoriev, Y. Petrukhin","doi":"10.12775/LLP.2019.031","DOIUrl":"https://doi.org/10.12775/LLP.2019.031","url":null,"abstract":"In this paper, we present a logic MML S5 n which is a combination of multilattice logic and modal logic S5. MML S5 n is an extension of Kamide and Shramko’s modal multilattice logic which is a multilattice analogue of S4. We present a cut-free hypersequent calculus for MML S5 n in the spirit of Restall’s one for S5 and develop a Kripke semantics for MML S5 n , following Kamide and Shramko’s approach. Moreover, we prove theorems for embedding MML S5 n into S5 and vice versa. As a result, we obtain completeness, cut elimination, decidability, and interpolation theorems for MML S5 n . Besides, we show the duality principle for MML S5 n . Additionally, we introduce a modification of Kamide and Shramko’s sequent calculus for their multilattice version of S4 which (in contrast to Kamide and Shramko’s original one) proves the interdefinability of necessity and possibility operators. Last, but not least, we present Hilbert-style calculi for all the logics in question as well as for a larger class of modal multilattice logics.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41749671","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：