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.

Modal Semantics without Possible Worlds

Abstract: ?1. Four values. In this paper I will develop a semantic account for modal logic by considering only the values of sentences (and formulas). This account makes no use of possible worlds. To develop such an account, we must recognize four values. These are obtained by subdividing (plain) truth into necessary truth (T) and contingent truth (t); and by subdividing falsity into contingent falsity (f) and necessary falsity (impossibility: F). The semantic account results from reflecting on these concepts and on the meanings of the logical operators. To begin with, we shall consider the propositional language Lo. The language Lo has (1) infinitely many atomic sentences, (2) the two truth-functional connectives %, V, and the modal operator Cl. (Square brackets are used for punctuation.) The other logical expressions are defined as follows: Dl [A&B] =(def)-[ -A V -B], D2 [A v B] (def)[-A V B], D3 0 A =(def)FIp-A. I shall use matrices to give partial characterizations of the significance of logical expressions in Lo. For negation, this matrix is wholly adequate:

Representing multiple theories

Abstract: Most Artificial Intelligence programs lack generality because they reason with a single domain theory that is tailored for a specific task and embodies a host of implicit assumptions. Contexts have been proposed as an effective solution to this problem by providing a mechanism for explicitly stating the assumptions underlying a domain theory. In addition, contexts can be used to focus reasoning, allow the representation of mutually incoherent domain theories, lift axioms from one context into another, and transcend a context. In this paper we develop a simple propositional logic of context suitable for representing and reasoning with multiple domain theories. We introduce contexts as modal operators, and allow different contexts to have different vocabularies. We analyze the computational properties of the logic, providing the central computational justification for the use of contexts. We show how the logic effectively handles the common uses of contexts. We also discuss the extensions needed to handle first-order logic.

Modal logics for qualitative possibility and beliefs

Abstract: Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.

The Convergence of Scientific Knowledge: A view from the limit

Abstract: List of Figures. List of Tables. Preface. Acknowledgments. Formal Prerequisites. Interdependence Scheme for Topics. 1. Introduction. Part I: The Philosophy of Convergence. 2. Knowledge, Method and Reliability. 3. Knowledge and Skepticism. 4. The Epistemology of Convergence. Part II: Modal Operator Theory. 5. The Ontology of Convergence. 6. Science and Setup. 7. Two Relations of Correctness. 8. Methods and Methodology. 9. Forcing. 10. Definitions of Knowledge. 11. Modal Formalization. 12. Systems for Convergent Knowledge. 13. Knowledge in Time. 14. Forcing, Convergence - and Method. 15. Transmissibility. Part III: Convergence In Sum. 16. Knowledge in the End. Appendices. Index. Nomenclature. References.

Roles, Rigidity, and Quantification in Epistemic Logic

Abstract: Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic: Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in Melvin Fitting’s First-Order Intensional Logic, that we argue solves these and other conceptual problems. Topics covered include: Quine on the “collapse” of modal distinctions; the rigidity of names; belief reports and unarticulated constituents; epistemic roles; counterfactual attitudes; representational versus interpretational semantics; ignorance of co-reference versus ignorance of identity; two-dimensional epistemic models; quantification into epistemic contexts; and an approach to multi-agent epistemic logic based on centered worlds and hybrid logic.