Generalized Update Semantics

Mind ◽  
2019 ◽  
Vol 128 (511) ◽  
pp. 795-835
Author(s):  
Simon Goldstein
Keyword(s):  
Modal Logic ◽  
Dynamic Semantics ◽  
Epistemic Modals ◽  
Kripke Semantics ◽  
Dynamic Update ◽  
Update Semantics ◽  
Construction Procedure ◽  
Special Cases ◽  
Truth Conditional ◽  
The Relationship

Abstract This paper explores the relationship between dynamic and truth conditional semantics for epistemic modals. It provides a generalization of a standard dynamic update semantics for modals. This new semantics derives a Kripke semantics for modals and a standard dynamic semantics for modals as special cases. The semantics allows for new characterizations of a variety of principles in modal logic, including the inconsistency of ‘p and might not p’. Finally, the semantics provides a construction procedure for transforming any truth conditional semantics for modals into a dynamic semantics for modals with similar properties.

Declarative sentences

2017 ◽  
Author(s):  
Sarah E. Murray
Keyword(s):  
Dynamic Semantics ◽  
Update Semantics ◽  
Truth Conditional

Chapter 4 develops a compositional implementation of this analysis for evidentials in declarative sentences that does not appeal to separate dimensions of illocutionary meaning. In particular, I use an update semantics where both truth‐conditional content and anaphoric potential is encoded (Update with Centering). The formal implementation builds on work in dynamic semantics and the semantics of assertion and questions. This compositional, dynamic implementation integrates the different kinds of semantic contributions discussed in Chapter 3 into a single representation of meaning.

scholarly journals Recursive enumerability and elementary frame definability in predicate modal logic

2019 ◽  
Vol 30 (2) ◽  
pp. 549-560 ◽  
Author(s):  
Mikhail Rybakov ◽  
Dmitry Shkatov
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
The Other ◽  
Kripke Semantics ◽  
First Order ◽  
Elementary Class ◽  
Recursive Enumerability ◽  
Kripke Frames ◽  
Recursively Enumerable ◽  
The Relationship

Abstract We investigate the relationship between recursive enumerability and elementary frame definability in first-order predicate modal logic. On one hand, it is well known that every first-order predicate modal logic complete with respect to an elementary class of Kripke frames, i.e. a class of frames definable by a classical first-order formula, is recursively enumerable. On the other, numerous examples are known of predicate modal logics, based on ‘natural’ propositional modal logics with essentially second-order Kripke semantics, that are either not recursively enumerable or Kripke incomplete. This raises the question of whether every Kripke complete, recursively enumerable predicate modal logic can be characterized by an elementary class of Kripke frames. We answer this question in the negative, by constructing a normal predicate modal logic which is Kripke complete, recursively enumerable, but not complete with respect to an elementary class of frames. We also present an example of a normal predicate modal logic that is recursively enumerable, Kripke complete, and not complete with respect to an elementary class of rooted frames, but is complete with respect to an elementary class of frames that are not rooted.

Epistemic modals and probability operators

2018 ◽  
Author(s):  
Sarah Moss
Keyword(s):  
Epistemic Modals ◽  
Full Belief ◽  
Probabilistic Semantics ◽  
Probability Operators ◽  
Probability Spaces ◽  
Truth Conditional ◽  
Simple Sentences ◽  
The Relationship ◽  
Semantic Values

This chapter defends a semantics for epistemic modals and probability operators. This semantics is probabilistic—that is, sentences containing these expressions have sets of probability spaces as their semantic values relative to a context. Existing non-truth-conditional semantic theories of epistemic modals face serious problems when it comes to interpreting nested modal constructions such as ‘it must be possible that Jones smokes’. The semantics in this chapter solves these problems, accounting for several significant features of nested epistemic vocabulary. The chapter ends by defending a probabilistic semantics for simple sentences that do not contain any epistemic vocabulary, and by using this semantics to illuminate the relationship between credence and full belief.

scholarly journals Concepts as Modalities in Description Logics

10.29007/9cxg ◽  
2019 ◽  
Author(s):  
Lukas Grätz
Keyword(s):  
Modal Logic ◽  
Description Logics ◽  
Kripke Semantics ◽  
Kripke Structure ◽  
Modal Operators ◽  
Colloquial Language ◽  
Future Work ◽  
The Relationship

Motivated by the colloquial language term of a “glass gummy bear”, an additional type of concept composition for description logics is suggested. This composition type is then axiomatically formalized and called concept generalization. Consistency of the formalization is checked. By proving axiom K and Go ̈del rule, it is shown that this logic is in fact a multi-modal logic. Concepts could be both modal operators and predicate symbols. A Kripke semantics is presented (the adequacy is future work). In this semantics, the TBox axioms hold for any view, assertions in the ABox hold for the natural view (a selected world in the Kripke structure) only. The relationship to other formalisms is outlined. Further examples are discussed at the end.

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

scholarly journals Surrogate Endpoint Evaluation: Principal Stratification Criteria and the Prentice Definition

2015 ◽  
Vol 3 (2) ◽  
pp. 157-175 ◽  
Author(s):  
Peter B. Gilbert ◽  
Erin E. Gabriel ◽  
Ying Huang ◽  
Ivan S.F. Chan
Keyword(s):  
Causal Effect ◽  
Surrogate Endpoint ◽  
Effect Modification ◽  
Principal Stratification ◽  
Clinical Endpoint ◽  
Efficacy Trial ◽  
Marker Selection ◽  
Special Cases ◽  
High Utility ◽  
The Relationship

AbstractA common problem of interest within a randomized clinical trial is the evaluation of an inexpensive response endpoint as a valid surrogate endpoint for a clinical endpoint, where a chief purpose of a valid surrogate is to provide a way to make correct inferences on clinical treatment effects in future studies without needing to collect the clinical endpoint data. Within the principal stratification framework for addressing this problem based on data from a single randomized clinical efficacy trial, a variety of definitions and criteria for a good surrogate endpoint have been proposed, all based on or closely related to the “principal effects” or “causal effect predictiveness (CEP)” surface. We discuss CEP-based criteria for a useful surrogate endpoint, including (1) the meaning and relative importance of proposed criteria including average causal necessity (ACN), average causal sufficiency (ACS), and large clinical effect modification; (2) the relationship between these criteria and the Prentice definition of a valid surrogate endpoint; and (3) the relationship between these criteria and the consistency criterion (i.e. assurance against the “surrogate paradox”). This includes the result that ACN plus a strong version of ACS generally do not imply the Prentice definition nor the consistency criterion, but they do have these implications in special cases. Moreover, the converse does not hold except in a special case with a binary candidate surrogate. The results highlight that assumptions about the treatment effect on the clinical endpoint before the candidate surrogate is measured are influential for the ability to draw conclusions about the Prentice definition or consistency. In addition, we emphasize that in some scenarios that occur commonly in practice, the principal strata subpopulations for inference are identifiable from the observable data, in which cases the principal stratification framework has relatively high utility for the purpose of effect modification analysis and is closely connected to the treatment marker selection problem. The results are illustrated with application to a vaccine efficacy trial, where ACN and ACS for an antibody marker are found to be consistent with the data and hence support the Prentice definition and consistency.

I Wasn’t Talking about That

Aboutness ◽  
2014 ◽  
Author(s):  
Stephen Yablo
Keyword(s):  
Subject Matter ◽  
Epistemic Modals ◽  
Empirical Adequacy ◽  
Independent Factor ◽  
Van Fraassen ◽  
Partial Truth ◽  
Truth Conditional ◽  
Ways Of Being

This chapter argues that partial truth is apt to strike us as sneaky, unclean, the last refuge of a scoundrel. But, whether a statement is partly true, or true in what it says about BLAH, may be all that we want to know. A statement S is partly true insofar as it has wholly true parts: wholly true implications whose subject matter is included in that of S. An account of subject matter will thus be needed, and of the relation (“aboutness”) that sentences bear to their subject matters, if we want to understand partial truth. Aboutness has been somewhat neglected in philosophy. But not entirely; think of Frege on identity, Kripke on counterparts, van Fraassen on empirical adequacy, Yalcin on epistemic modals, and Hempel on confirmation. Subject matter will be treated here as an independent factor in meaning, over and above truth-conditional content. Not completely independent, though, for what a sentence is about is tied up with its ways of being true and false.

scholarly journals Addition Formula and Related Integral Equations for Heine—Stieltjes Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1231
Author(s):  
Hans Volkmer
Keyword(s):  
Integral Equations ◽  
Explicit Form ◽  
Spherical Harmonics ◽  
Reproducing Kernel ◽  
Addition Formula ◽  
Symmetric Products ◽  
Special Cases ◽  
Related Integral ◽  
Generalized Spherical Harmonics ◽  
The Relationship

It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found.

An analysis of the variation between dairy-sire progeny-groups for milk yield and fat content

1958 ◽  
Vol 1958 ◽  
pp. 19-29 ◽  
Author(s):  
Alan Robertson ◽  
S. S. Khishin
Keyword(s):  
Milk Yield ◽  
Comparison Method ◽  
Fat Content ◽  
Fat Percentage ◽  
Simple Method ◽  
Factors Affecting ◽  
Special Cases ◽  
The Mean ◽  
Milk Marketing ◽  
The Relationship

The past few years have seen the development in Great Britain of the ‘contemporary comparison’ method for evaluating progeny tests of dairy sires (Macarthur, 1954; Robertson, Stewart and Ashton 1956). The final overall figure attached to a sire is the mean difference between the yield of his daughters and that of other heifers milking in the same herd in the same year, with due regard for the numbers of animals in the two groups. Although it has some imperfections in special cases, this is probably the most informative simple method of evaluating a sire for yield and, fortunately, one which could be easily integrated with the existing recording system. The method has been turned into a simple routine in the Bureau of Records of the Milk Marketing Board and several thousand bulls have now been evaluated. In this paper, we shall be mostly concerned to use this material to investigate the heritabilities of milk yield and fat content and the relationship between the two in the different breeds. The information that we shall use consists, for each bull, of the mean contemporary comparison, with its effective ‘weight’, and the average fat percentage of the daughters. Before we deal with the observed results, we should go into rather more detail into the nature of these two figures and into the factors affecting them.

scholarly journals Counterpart theories for everyone

Synthese ◽  
2020 ◽  
Vol 197 (11) ◽  
pp. 4691-4715
Author(s):  
Achille C. Varzi
Keyword(s):  
Modal Logic ◽  
Semantic Theory ◽  
Counterpart Theory ◽  
Philosophical Significance ◽  
Special Cases ◽  
Identity Based

Abstract David Lewis’s counterpart theory (CT) is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic (ML), suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions (all worlds are equally real, individuals are world-bound) that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted.

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