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.

Epistemic logic without closure

Abstract: All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not be so. The abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure.

Modal Verbs in the Common Ground: Discriminating Among Actual and Nonactual Uses of Could and Would for Improved Text Interpretation

Abstract: Modal verbs occur in contexts which convey information about non-actual states of affairs as well as in contexts which convey information about the actual world of the discourse. Modeling the semantic interpretation of non-actual states of affairs is notoriously complicated, sometimes requiring modal logic, belief revision, non-monotonic reasoning, and multi-agent autoepistemic models. This work presents linguistic features which disambiguate those instances of the past tense modal verbs `could’ and `would’ which occur in contexts where the proposition in the scope of the modal is not true in the actual world of the discourse from those instances which presuppose or entail that an event in their scope occurred in the actual world of the discourse. It also illustrates the complexity of the role of modal verbs in semantic interpretation and, consequently, the limitations of state of the art inference systems with respect to modal verbs. The features suggested for improving modal verb interpretation are based on the analysis of corpus data and insights from the linguistic literature.

Actualism and modal semantics

Abstract: According to actualism, modal reality is constructed out of valuations (combinations of truth values for all propositions). According to possibilism, modal reality consists in a set of possible worlds, conceived as independent objects that assign truth values to propositions. According to possibilism, accounts of modal reality can intelligibly disagree with each other even if they agree on which valuations are contained in modal reality. According to actualism, these disagreements (possibilist disagreements) are completely unintelligible. An essentially actualist semantics for modal propositional logic specifies which sets of valuations are compatible with the meanings of the truth-functional connectives and modal operators without drawing on formal resources that would enable us to represent possibilist disagreements. The paper discusses the availability of an essentially actualist semantics for modal propositional logic. I argue that the standard Kripkean semantics is not essentially actualist and that other extant approaches also fail to provide a satisfactory essentially actualist semantics. I end by describing an essentialist actualist semantics for modal propositional logic.

Decidable Navigation Logics for Object Structures

Abstract: In this paper, we introduce decidable multimodal logics to describe and reason about navigation across object structures. The starting point of these navigation logics is the modelling of object structures as Kripke models that contain a family of deterministic accessibility relations; one for each pointer attribute. These pointer attributes are used in the logics both as first-order terms in equalities and as modal operators. To handle the ambiguities of pointer attributes the logics also cover a mechanism to bind logical variables to objects that are reachable by a pointer. The main result of this paper is a tableau construction for deciding the validity of formulas in the navigation logics.