Topic
Modal operator
About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.
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01 Jan 2005
TL;DR: This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation, which can be seen as a kind of modal logic with a twoplace modal operator, the relevant conditional.
Abstract: : This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a twoplace modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s presentation of the completeness proof quite closely [10]), but with an important twist, to do with the absence of Boolean negation.
TL;DR: In this article, a criterion of finite detachment-substitutional formalization for normal modal systems is proposed, which is based on substitution, detachment for material implication and Godel rules.
Abstract: The aim of this paper is to propose a criterion of finite detachment-substitutional formalization for normal modal systems. The criterion will comprise only those normal modal systems which are finitely axiomatizable by means of the substitution, detachment for material implication and Godel rules.
01 Jan 2017
TL;DR: The chapter goes on to develop the idea of it being possible for a quantity to be such-and-such, which is introduced to deal with claims difficult to capture with conventional sentential modal operators.
Abstract: Modal features of quantities are discussed in the final chapter. Talk of atomic number as the essence of something, unclear exactly what, is put aside in favour of pursuing Paneth’s more fruitful distinction between elements as simple and as basic, leading to a discussion of how resilient being the same element is to possible changes in states of combination. The chapter goes on to develop the idea of it being possible for a quantity to be such-and-such, which is introduced to deal with claims difficult to capture with conventional sentential modal operators. This leads to the replacement of a model theory of possible worlds by the explicit quantification over possible states to achieve appropriate expressive power. Incorporation of possible processes is a natural development, linking up with the discussion in the previous chapter. The interplay between possibility and time is developed, keeping track of the time when a possibility arises and the time when it is possible for a quantity of have a property or be related to something.
TL;DR: A finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given and is proved to be sound and strongly complete.
Abstract: Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.
TL;DR: Knowledge modal formulas are interpreted by a universal modal world in the hypersets universe [A], where each world can interpret only a portion of knowledge modal formula as mentioned in this paper, and this remedy the limitation of the interpretation of knowledge formulas by a tower of modal worlds in the well founded universe.
Abstract: Knowledge modal formulas are interpreted by a universal modal world in the hypersets universe [A]. This remedies the limitation of the interpretation of knowledge formulas by a tower of modal worlds in the well founded universe [F], where each world can interpret only a portion of knowledge modal formulas.