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.

Basic logic for ontic and deontic modalities

Abstract: The difficulty to interpret the iteration of modalities, already ontic and still more deontic, incites to pay attention to the system B of basic modal logic that John L. Pollock proposed in 1967. The Pollock’s system brought all the theses which, in the classical ontic modal systems, from Sl to S5, contain no iteration of the modal functors. With this basic ontic system we characterize a basic deontic system, and a basic ontico-deontic system, the former including all the theses of the first two. Each of the three systems is based axiomatically and assorted with a semantics for which the soundness and the completeness hold. In [6] John L. Pollock proposed a basic modal logic, B, whose main characteristics was that it did not admit any iterated modality, i.e. no modal operator would appear within the scope of another modality. The system B 1 may be based on two axioms: A1 Lp ⊃ p A2 L(p ⊃ q) ⊃ (Lp ⊃ Lq) and the four inference rules: R1 Rule of substitution, proviso that the substitution of a WFF (well formed formula) does not generate any iteration of modality R2 Rule of replacement, with the classical definitions of PC (propositional calculus) and the definition

Models, Modality, and Natural Theology

Abstract: In the Logic of Perfection, Charles Hartshorne developed what has come to be known as the modal ontological proof for the existence of God.1 That proof relies on two premises, the first of which is that God’s existence is not contingent (rendered in modal logic as), 1| ~CG, and the second of which is that God’s existence is possible, 2| MG (where ‘G’ is some version of the assertion “God exists”, ‘C’ is a modal operator representing “it is contingent that…”, and ‘M’ is the model operator for representing possibility). In modal logic, ‘Cp’ is defined as

The Truth About Predicates and Connectives

Abstract: In his rich “The Truth Predicate vs. the Truth Connective. On taking connectives seriously.’’ Kevin Mulligan (2010) starts an inquiry into the logical form of truth ascriptions and challenges the prevailing view which takes truth ascriptions to be of subject predicate form, that is a truth predicate applied to a name of a proposition or sentence. In this chapter we shall first discuss Mulligan’s proposal from the perspective of linguistics and, especially, syntax theory. Even though theory of syntax provides little evidence for Mulligan’s view, we shall argue that this does not disqualify the thesis that it is a truth connective (or operator as we shall frequently say) which figures in the logical form of truth ascriptions. We shall then look at the distinction between sentential predicates and sentential operators from a more logical point of view. It is often thought that we should opt for modal operators so the self-referential paradoxes are avoided. We argue that whether paradox will arise is not a question of grammatical category but of the expressive power of the approach.

Combining circumscription and modal logic

Abstract: This paper discusses the logic LKM which extends circumscription into an epistemic domain. This extension will allow us to define circumscription of predicates that appear within the context of a modal operator. In fact, LKM can be seen as a method of extending any first-order nonmonotonic logic whose semantic definition is based on a partial-order among models, into a new nonmonotonic logic defined for a modal language, whose modal operator (K) follows an undedying S5 or weak-S5 semantics. One interesting use of this nonmonotonic logic is to model nonmonotonic aspects of the communication between agents.

Reasoning about data-parallel pointer programs in a modal extension of separation logic

Abstract: This paper proposes a modal extension of Separation Logic [1,2] for reasoning about data-parallel programs that manipulate heap allocated linked data structures. Separation Logic provides a formal means for expressing allocation of disjoint substructures, which are to be processed in parallel. A modal operator is also introduced to relate the global property of a parallel operation with the local property of each sequential execution running in parallel. The effectiveness of the logic is demonstrated through a formal reasoning on the parallel list scan algorithm featuring the pointer jumping technique.