scholarly journals Different Arguments, Same Problems

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.

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

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.

scholarly journals Two nondescriptivist views of normative and evaluative statements

2018 ◽  
Vol 48 (3-4) ◽  
pp. 405-424 ◽  
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.

Modal operators on bounded commutative residuated ℓ-monoids

2007 ◽  
Vol 57 (4) ◽  
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.

scholarly journals Quantified Temporal Alethic Boulesic Doxastic Logic

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.

Suppose and Tell

2020 ◽  
Author(s):  
Timothy Williamson
Keyword(s):  
Conditional Probability ◽  
Natural Deduction ◽  
Special Kind ◽  
Context Sensitivity ◽  
Modal Operator ◽  
Counterfactual Conditionals ◽  
Deduction Rules ◽  
Psychological Sense

The book argues that our use of conditionals is governed by imperfectly reliable heuristics, in the psychological sense of fast and frugal (or quick and dirty) ways of assessing them. The primary heuristic is this: to assess ‘If A, C’, suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’. This heuristic yields both the equation of the probability of ‘If A, C’ with the conditional probability of C on A and standard natural deduction rules for the conditional. However, these results can be shown to make the heuristic implicitly inconsistent, and so less than fully reliable. There is also a secondary heuristic: pass conditionals freely from one context to another under normal conditions for acceptance of sentences on the basis of memory and testimony. The effect of the secondary heuristic is to undermine interpretations on which ‘if’ introduces a special kind of context-sensitivity. On the interpretation which makes best sense of the two heuristics, ‘if’ is simply the truth-functional conditional. Apparent counterexamples to truth-functionality are artefacts of reliance on the primary heuristic in cases where it is unreliable. The second half of the book concerns counterfactual conditionals, as expressed with ‘if’ and ‘would’. It argues that ‘would’ is an independently meaningful modal operator for contextually restricted necessity: the meaning of counterfactuals is simply that derived compositionally from the meanings of their constituents, including ‘if’ and ‘would’, making them contextually restricted strict conditionals.

scholarly journals Formula size games for modal logic and μ-calculus

2019 ◽  
Vol 29 (8) ◽  
pp. 1311-1344 ◽  
Author(s):  
Lauri T Hella ◽  
Miikka S Vilander
Keyword(s):  
Modal Logic ◽  
Optimal Strategy ◽  
Order Logic ◽  
First Order Logic ◽  
Kripke Models ◽  
First Order ◽  
Modal Operators ◽  
Crucial Difference ◽  
Definition Of ◽  
Person Game

Abstract We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $\textrm{FO}$ and (basic) modal logic $\textrm{ML}$. We also present a version of the game for the modal $\mu $-calculus $\textrm{L}_\mu $ and show that $\textrm{FO}$ is also non-elementarily more succinct than $\textrm{L}_\mu $.

On finite and infinite modal systems

1938 ◽  
Vol 3 (2) ◽  
pp. 77-82 ◽  
Author(s):  
C. West Churchman
Keyword(s):  
Modal Logic ◽  
Symbolic Logic ◽  
Modal Operator ◽  
Image Position ◽  
Modal Systems ◽  
Complex Modal

In Oskar Becker's Zur Logik der Modalitäten four systems of modal logic are considered. Two of these are mentioned in Appendix II of Lewis and Langford's Symbolic logic. The first system is based on A1–8 plus the postulate,From A7: ∼◊p⊰∼p we can prove the converse of C11 by writing ∼◊p for p, and hence deriveThe addition of this postulate to A1–8, as Becker points out, allows us to “reduce” all complex modal functions to six, and these six are precisely those which Lewis mentions in his postulates and theorems: p, ∼p, ◊p, ∼◊p, ∼◊∼p, and ◊∼p This reduction is accomplished by showingwhere ◊n means that the modal operator ◊ is repeated n times; e.g., ◊3p = ◊◊◊p. Then it is shown thatBy means of (1), (2), and (3) any complex modal function whatsoever may be reduced to one of the six “simple” modals mentioned above.It might be asked whether this reduction could be carried out still further, i.e., whether two of the six “irreducible” modals could not be equated. But such a reduction would have to be based on the fact that ◊p = p which is inconsistent with the set B1–9 of Lewis and Langford's Symbolic logic and independent of the set A1–8. Hence for neither set would such a reduction be possible.

Grading Modal Judgement

Mind ◽  
2019 ◽  
Vol 129 (515) ◽  
pp. 769-807
Author(s):  
Nate Charlow
Keyword(s):  
Epistemic Modality ◽  
New Model ◽  
Alternative Models ◽  
Modal Operators ◽  
Modal Claim ◽  
Plausible Model ◽  
Normative Epistemology

Abstract This paper proposes a new model of graded modal judgement. It begins by problematizing the phenomenon: given plausible constraints on the logic of epistemic modality, it is impossible to model graded attitudes toward modal claims as judgements of probability targeting epistemically modal propositions. This paper considers two alternative models, on which modal operators are non-proposition-forming: (1) Moss (2015), in which graded attitudes toward modal claims are represented as judgements of probability targeting a ‘proxy’ proposition, belief in which would underwrite belief in the modal claim; (2) a model on which graded attitudes toward modal claims are represented as judgements of credence taking as their objects (non-propositional) modal representations (rather than proxy propositions). The second model, like Moss’s model, is shown to be semantically and mathematically tractable. The second model, however, can be straightforwardly integrated into a plausible model of the role of graded attitudes toward modal claims in cognition and normative epistemology.

scholarly journals The effect of English Non-Modal Operators on Proficiency and Performance of Undergraduate Students

2020 ◽  
Vol 4 (1) ◽  
pp. 271-281
Author(s):  
Khalid ◽  
Ghani Rahman ◽  
Abdul Hamid
Keyword(s):  
Data Collection ◽  
Undergraduate Students ◽  
Proficiency Test ◽  
Sampling Technique ◽  
Model Operator ◽  
Undergraduate Level ◽  
Modal Operators ◽  
Idiomatic Expressions ◽  
Convenience Sampling ◽  
And Performance

This study focuses on the problems posed by the English non-modal operators to the undergraduate level students of Hazara University, Mansehra, Pakistan. The data was collected from hundred students selected through non-random and convenience sampling technique. A proficiency test was used as a tool for data collection. The test was focused on all the uses of non-modal operators. The results show that some of these problems were caused by the intervention of some of grammatical concepts like tense, aspect, back shifting and voice. While some grammatical operations like negation, interrogation and insertion/omission had no role and so were found comparatively easy. These operators when used after wh-word such as when, while, before and if posed difficulty for the subjects. Similarly, different forms such as non-tensed form and uses such as dynamic and non-dynamic of non-modal operators were also problematic for the subjects. The highest frequency of error was found in the use of non-model operator for emphasis and surprise. However, the degree of difficulty posed by non-modal operators in idiomatic expressions was not significant.

scholarly journals Mínimo e máximo em estruturas nominais – uma análise semântica

2019 ◽  
pp. 250-264
Author(s):  
Rui Marques
Keyword(s):  
Possible Worlds ◽  
Modal Operator ◽  
Possible World

This paper is concerned with the semantics of the portuguese phrases with the form o mínimo/máximo N (‘the minimum N’) and o mínimo/máximo de N (‘the minimum/maximum of N’). Some nouns may occur in both of these constructions, while others might occur in only one of them, and still other nouns might occur only if accompanied by a modal operator. The proposal is made that these facts can be straightforwardly explained by the hypothesis that the first and the second of these syntactic constructions have, respectively, an extensional and an intensional meaning, together with the fact that some nouns have the same denotation in any possible world, while others denote different sets of entities in different possible worlds.

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