scholarly journals Modal operators for meet-complemented lattices

2017 ◽  
Vol 25 (4) ◽  
pp. 465-495 ◽  
Author(s):  
José Luis Castiglioni ◽  
Rodolfo C. Ertola-Biraben
Keyword(s):  
Modal Operators ◽  
Complemented Lattices

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 $.

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

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 On the Difference between the Two Barbaras

Problemos ◽  
2018 ◽  
Vol 93 ◽  
pp. 90-101
Author(s):  
Živilė Pabijutaitė
Keyword(s):  
Full Article ◽  
Major Premise ◽  
English Only ◽  
Modal Operators ◽  
De Dicto ◽  
Modal Syllogistic ◽  
The Difference ◽  
Article Abstract

[full article, abstract in English; only abstract in Lithuanian] The paper deals with the problem of the “two Barbaras” in the Aristotelian modal syllogistic. The problem consists in Aristotle’s differing views on two at a first sight similar in nature syllogisms of mixed assertoric (X) and necessary (L) premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held to be invalid, or 2) negatively, because both Barbaras have been held to be valid, or 3) positively, by giving a reason why the two Barbaras differ. We commit ourselves to the position (3) by proving that modal propositions for Aristotle have their modalities de dicto and that Aristotelian modal operators act according to their own separate rules where only the type of the modality of a major premise is relevant for the modal status of the conclusion.

scholarly journals On the Decidability of Intuitionistic Tense Logic without Disjunction

2020 ◽  
Author(s):  
Fei Liang ◽  
Zhe Lin
Keyword(s):  
Proof Theory ◽  
Tense Logic ◽  
Heyting Algebras ◽  
Finite Model ◽  
Algebraic Proof ◽  
Model Property ◽  
Algebraic Models ◽  
Finite Axiomatizability ◽  
Finite Model Property ◽  
Modal Operators

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

κ-Complete Uniquely Complemented Lattices

Order ◽  
2008 ◽  
Vol 25 (2) ◽  
pp. 121-129
Author(s):  
John Harding
Keyword(s):  
Complemented Lattices ◽  
Uniquely Complemented
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