286,326 research outputs found
Alternative axiomatics and complexity of deliberative STIT theories
We propose two alternatives to Xu's axiomatization of the Chellas STIT. The
first one also provides an alternative axiomatization of the deliberative STIT.
The second one starts from the idea that the historic necessity operator can be
defined as an abbreviation of operators of agency, and can thus be eliminated
from the logic of the Chellas STIT. The second axiomatization also allows us to
establish that the problem of deciding the satisfiability of a STIT formula
without temporal operators is NP-complete in the single-agent case, and is
NEXPTIME-complete in the multiagent case, both for the deliberative and the
Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding
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Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic
This paper sets out a predicative response to the Russell-Myhill paradox of
propositions within the framework of Church's intensional logic. A predicative
response places restrictions on the full comprehension schema, which asserts
that every formula determines a higher-order entity. In addition to motivating
the restriction on the comprehension schema from intuitions about the stability
of reference, this paper contains a consistency proof for the predicative
response to the Russell-Myhill paradox. The models used to establish this
consistency also model other axioms of Church's intensional logic that have
been criticized by Parsons and Klement: this, it turns out, is due to resources
which also permit an interpretation of a fragment of Gallin's intensional
logic. Finally, the relation between the predicative response to the
Russell-Myhill paradox of propositions and the Russell paradox of sets is
discussed, and it is shown that the predicative conception of set induced by
this predicative intensional logic allows one to respond to the Wehmeier
problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi
A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD,
based on an extension of classical propositional logic with dependence atoms
plus dependence quantifiers treated as modalities, within the setting of
generalized assignment semantics for first order logic. The expressive
strength, complete proof calculus and meta-properties of LFD are explored.
Various language extensions are presented as well, up to undecidable
modal-style logics for independence and dynamic logics of changing dependence
models. Finally, more concrete settings for dependence are discussed:
continuous dependence in topological models, linear dependence in vector
spaces, and temporal dependence in dynamical systems and games.Comment: 56 pages. Journal of Philosophical Logic (2021
Neutral Free Logic: Motivation, Proof Theory and Models
Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka The Journal of Philosophy, 56, 125-137 1959;Lambert Notre Dame Journal of Formal Logic, 8, 133-144 1967, 1997, 2001). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free logics reject the claim that names need to denote in (ii). Positive free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, negative free logic treats them as uniformly false, and neutral free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (Bulletin of the Section of Logic, 48(2), 137-158 2019) as well as classical logic in Pavlovi and Gratzl (Journal of Philosophical Logic, 50, 117-148 2021), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (Studia Logica, 105(1), 93-119 2017, Journal of Applied Non-Classical Logics, 30(3), 272-289 2020), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties
Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics
This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here.
[9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic (2020). Online. Print publication forthcoming
Impossibility Results for Infinite-Electorate Abstract Aggregation Rules
Herzberg F, Eckert D. Impossibility Results for Infinite-Electorate Abstract Aggregation Rules. Journal of Philosophical Logic. 2012;41(1):273-286
Fuzzy Sets, Fuzzy Logic and Their Applications 2020
The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity
Логическая теория, построенная геометрическим образом
This paper scrutinizes Peirce’s Existential Graph Theory. It analyses its deductive part, viz. the rules of graphs transformations. The rules application is graphically introduced. Their validity is demonstrated informally. Such style reminds Peirce’s manner. Moreover, it reflects the originality of the theory, as well as it stresses its philosophical background. The contribution is a continuation of “Peirce's Graphs: Peculiarities of Construction and Interpretation” that was recently published in “Logic-Philosophical Studies” journal (Issue 14). Similar to the previous publication it mainly deals with alpha and beta graphs.Статья посвящена теории экзистенциальных графов Ч.С. Пирса. В работе анализируется свод правил, образующих дедуктивную часть теории. Работа правил демонстрируется графически, а их правомерность обосновывается неформально. Такой способ напоминает стиль самого Пирса. Кроме того, он наилучшим образом передает оригинальность теории, а также подчеркивает ее философскую основу. Данная работа является продолжением статьи «Графы Пирса: особенности построения и прочтения» о природе графов, опубликованной в 14-ом выпуске альманаха «Логико-философские штудии». В центре внимания по-прежнему оказываются разделы альфа и бета
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Relative Necessity and Propositional Quantification
AbstractFollowing Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.</jats:p
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