一个匹配生成更新语义的条件句系统

条件句系统通常用择类语义来刻画,此语义对条件句逻辑来说是标准的。一个择类模型可以用一个三元组（W,f,V）来表示,其中W≠Φ,f是从P（W）×W到P（W）中的择类函数,且V是从一命题变元集PV到P（W）中的赋值函数。本文我们提出一个更新语义,它保留择类框架,但V被从PV到P（W）^P（W）中的一个更新函数代替,因为更新函数能表示动态命题而赋值函数则不能。最后我们证明一个条件句系统相对这样的语义有框架可靠性。     

Uncertainty and Persistence: a Bayesian Update Semantics for Probabilistic Expressions

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent (i.e. beliefs that won’t necessarily survive the addition of new information that is compatible with all previous information), whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave.     

Kripke Bundle Semantics and C-set Semantics

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics.     

Wittgensteinian Semantics

Wittgenstein emphasizes two points concerning his notion of family resemblance. One is that the use of a family resemblance expression resists characterization by certain kinds of rules; the other is that due to the prevalence of family resemblance in the philosophical lexicon, philosophical inquiry must in many cases proceed differently from how it traditionally has. This paper develops an interpretation of family resemblance that seeks to do justice to these claims. I argue that what is characteristic about family resemblance expressions is not that they exhibit a basic semantic feature unique to themselves, but that they combine a number of semantic properties that happen not to be coinstantiated elsewhere. These features include (1) content variability (also a property of ambiguous expressions, polysemes, and standard indexicals), (2) a feature I call "topicality" (which is also a characteristic of polysemes), and (3) "semantic openness" (a feature of many ordinary indexicals). The notions of topicality and semantic openness are explained, and certain terms of natural language are shown to be family resemblance expressions. I conclude by indicating some of the potential philosophical ramifications of these results.     

Anti-Realist Semantics

I argue that the implementation of theDummettian program of an ``anti-realist' semanticsrequires quite different conceptions of the technicalmeaning-theoretic terms used than those presupposed byDummett. Starting from obvious incoherences in anattempt to conceive truth conditions as assertibilityconditions, I argue that for anti-realist purposesnon-epistemic semantic notions are more usefully kept apart from epistemic ones rather than beingreduced to them. Embedding an anti-realist theory ofmeaning in Martin-Löf's Intuitionistic Type Theory(ITT) takes care, however, of many notorious problemsthat have arisen in trying to specify suitableintuitionistic notions of semantic value,truth-conditions, and validity, taking into accountthe so-called ``defeasibility of evidence' forassertions in empirical discourses.     

Free Semantics

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic focussed upon, but the results extend to MC. The semantics is called ‘free semantics’ since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such ‘witnesses’ are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady’s normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system.     

Inferentializing Semantics

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of proof-theoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones.     

Relational Semantics and Domain Semantics for Epistemic Modals

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions.     

Measurement Theoretic Semantics And The Semantics Of Necessity

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement (e.g., of length). Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: (i) I show thatthe measurement theoretic framework is consistent with a robust (non-Quinean) view of modal logic, (ii) I give an account of the semantics of the modal notions within this framework, and (iii) I defend the suggested account against various objections.     

On the Treatment of Incomparability in Ordering Semantics and Premise Semantics

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate all these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals.     

Single Scoreboard Semantics

Philosophical Studies -