Probability as a modal operator: the possibilities of its combination with other modalities

Logic Journal of IGPL ◽

10.1093/jigpal/jzz044 ◽

2020 ◽

Author(s):

Nino Guallart

Keyword(s):

Subjective Probability ◽

Modal Operator ◽

Relational Semantics ◽

Modal Operators ◽

Probabilistic Semantics ◽

Probability Operator

Abstract In this work we examine some of the possibilities of combining a simple probability operator with other modal operators, in particular with a belief operator. We will examine the semantics of two possible situations for expressing probabilistic belief or the lack of it, a simple subjective probability operator (SPO) versus the composition of a belief operator, plus an objective modal operator (BOP). We will study their interpretations in two probabilistic semantics: a relational Kripkean one and a variation of neighbourhood semantics, showing that the latter is able to represent the lack of probabilistic belief more directly, just with the SPO, whereas relational semantics needs the combination of BOP probability to represent lack of belief.

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Different Arguments, Same Problems

European journal of analytic philosophy ◽

10.31820/ejap.13.2.1 ◽

2018 ◽

Vol 13 (2) ◽

pp. 5-22

Author(s):

Rafal Urbaniak

Keyword(s):

Propositional Variable ◽

Modal Operator ◽

Modal Operators

I illustrate with three classical examples the mistakes arising from using a modal operator admitting multiple interpretations in the same argument; the flaws arise especially easily if no attention is paid to the range of propositional variables. Premisses taken separately might seem convincing and a substitution for a propositional variable in a modal context might seem legitimate. But there is no single interpretation of the modal operators involved under which all the premisses are plausible and the substitution successful.

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Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

Journal of Philosophical Logic ◽

10.1007/s10992-021-09638-0 ◽

2022 ◽

Author(s):

Frederik Van De Putte ◽

Dominik Klein

Keyword(s):

Expressive Power ◽

Modal Logics ◽

Relational Semantics ◽

Modal Operators

AbstractWe study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational semantics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.

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Neighborhood Semantics for Logics of Unknown Truths and False Beliefs

The Australasian Journal of Logic ◽

10.26686/ajl.v14i1.4033 ◽

2017 ◽

Vol 14 (1) ◽

Cited By ~ 1

Author(s):

David Gilbert ◽

Giorgio Venturi

Keyword(s):

Modal Operator ◽

Relational Semantics ◽

False Beliefs ◽

Semantic Approach ◽

Neighborhood Semantics ◽

Neighborhood Structures ◽

The Relationship

This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics (RI-logics) and logics containing the provability operator as the primary modal operator.

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Two nondescriptivist views of normative and evaluative statements

Canadian Journal of Philosophy ◽

10.1080/00455091.2018.1432400 ◽

2018 ◽

Vol 48 (3-4) ◽

pp. 405-424 ◽

Cited By ~ 1

Author(s):

Matthew Chrisman

Keyword(s):

Final Section ◽

Attractive Alternative ◽

Alternative Route ◽

Modal Operator ◽

Modal Operators ◽

Normative Language ◽

Evaluative Language ◽

Normative Term

AbstractThe dominant route to nondescriptivist views of normative and evaluative language is through the expressivist idea that normative terms have distinctive expressive roles in conveying our attitudes. This paper explores an alternative route based on two ideas. First, a core normative term ‘ought’ is a modal operator; and second, modal operators play a distinctive nonrepresentational role in generating meanings for the statements in which they figure. I argue that this provides for an attractive alternative to expressivist forms of nondescriptivism about normative language. In the final section of the paper, I explore ways it might be extended to evaluative language.

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Modal operators on bounded commutative residuated ℓ-monoids

Mathematica Slovaca ◽

10.2478/s12175-007-0026-3 ◽

2007 ◽

Vol 57 (4) ◽

Cited By ~ 6

Author(s):

Jiří Rachůnek ◽

Dana Šalounová

Keyword(s):

Fuzzy Logic ◽

Residuated Lattice ◽

Heyting Algebras ◽

Modal Operator ◽

Modal Operators ◽

Special Cases ◽

Basic Fuzzy Logic ◽

Commutative Residuated Lattice ◽

Derived Algebras ◽

Mv Algebras

AbstractBounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVÁ,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.

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Quantified Temporal Alethic Boulesic Doxastic Logic

Logica Universalis ◽

10.1007/s11787-020-00264-z ◽

2020 ◽

Author(s):

Daniel Rönnedal

Keyword(s):

Temporal Part ◽

Modal Operator ◽

Doxastic Logic ◽

Modal Operators ◽

Semantic Tableaux ◽

The Will ◽

Tableau System ◽

Historical Necessity ◽

Theoretical Apparatus ◽

Different Parts

Abstract The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of $$T \times W$$ T × W models, and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

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Probabilistic Semantics, Identity and Belief

Canadian Journal of Philosophy ◽

10.1080/00455091.1983.10715842 ◽

1983 ◽

Vol 13 (3) ◽

pp. 353-364 ◽

Cited By ~ 2

Author(s):

William Seager

Keyword(s):

Subjective Probability ◽

Probability Function ◽

Truth Conditions ◽

Probability Functions ◽

Probabilistic Semantics ◽

Rational Individual ◽

The Individual

The goal of standard semantics is to provide truth conditions for the sentences of a given language. Probabilistic Semantics does not share this aim; it might be said instead, if rather cryptically, that Probabilistic Semantics aims to provide belief conditions.The central and guiding idea of Probabilistic Semantics is that each rational individual has ‘within’ him or her a personal subjective probability function. The output of the function when given a certain sentence as input represents the degree of likelihood which the individual would assign to that sentence. One can characterize these functions via a set of axioms, and in the terms of this defined structure develop probabilistic analogues of all important semantical notions (e.g. validity, entailment). Then, dealing with ‘being given probability 1’ instead of ‘truth,’ one can proceed to give a completely adequate semantics for the particular language under consideration. The axioms delimiting the class of probability functions are, in fact, chosen with this goal and language in mind.

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