A New Semantics for Systems of Logic of Essence

The purpose of the present paper is to provide a way of understanding systems of logic of essence by introducing a new semantic framework for them. Three central results are achieved: first, the now standard Fitting semantics for the propositional logic of evidence is adapted in order to provide a new, simplified semantics for the propositional logic of essence; secondly, we show how it is possible to construe the concept of necessary truth explicitly by using the concept of essential truth; finally, Fitting semantics is adapted in order to present a simplified semantics for the quantified logic of essence.     

Game theoretical semantics and entailment

The essence of the meaning of a declarative sentence is given by stating its truth conditions, and consequently semantics, the study of meaning, must include a theory of truth conditions. Such a theory must not only describe accurately the truth conditions of declarative sentences, it must also answer the question of when two sentences have the same truth conditions. The fundamental semantic relation of having the same truth conditions cannot be ignored by any reasonable theory.This paper is an attempt to find a partial account of this relation by using game theoretical semantics as developed by Hintikka and his followers. The account given will establish a connection between this approach to semantics and the theory of firstdegree entailment formulated by Anderson and Belnap.     

RIGID DESIGNATION, DIRECT REFERENCE, AND MODAL METAPHYSICS

Abstract:  In this paper I argue that questions about the semantics of rigid designation are commonly and illicitly run together with distinct issues, such as questions about the metaphysics of essence and questions about the theoretical legitimacy of the possible-worlds framework. I discuss in depth two case studies of this phenomenon – the first concerns the relation between rigid designation and reference, the second concerns the application of the notion of rigidity to general terms. I end by drawing out some conclusions about the relations between rigid designation, semantic frameworks, reference, and essence.     

现代本质主义的逻辑基础与哲学意蕴

<正>现代分析哲学家致力于意义的分析,力图通过对语言的分析使哲学科学化。以罗素和逻辑实证主义为代表的前期分析哲学家拒斥一切形而上学,所有导致本质主义的学说均被他们宣布为虚妄。但到     

Luther's Trinitarian Hermeneutic and the Old Testament

In this study, the author shows that Luther's trinitarian understanding is shaped by the royal Psalms' dialogical model as well as informed by a hermeneutics that moors a trinitarian semantics in the Hebrew text of the Old Testament. The analysis concentrates on Luther's translation into German of two Hebrew names for God and of passages classically associated with the trinitarian doctrine (Psalm 110:1; Psalm 2:2.12). The result is a trinitarian structure of transparency. The text's syntax, narrative and direct speech mirror literally the transparency of the divine essence through the distinguishing characteristics of each trinitarian person.     

Luther’s Trinitarian Hermeneutic and the Old Testament

In this study, the author shows that Luther’s trinitarian understanding is shaped by the royal Psalms’ dialogical model as well as informed by a hermeneutics that moors a trinitarian semantics in the Hebrew text of the Old Testament. The analysis concentrates on Luther’s translation into German of two Hebrew names for God and of passages classically associated with the trinitarian doctrine (Psalm 110:1; Psalm 2:2.12). The result is a trinitarian structure of transparency. The text’s syntax, narrative and direct speech mirror literally the transparency of the divine essence through the distinguishing characteristics of each trinitarian person.     

Dissociative effects of stimulus quality on semantic and morphological contexts in visual word recognition.

Semantic and morphological contexts were manipulated jointly with stimulus quality under conditions where there were few related prime-target pairs (i.e., low relatedness proportion) in a lexical decision experiment. Additive effects of semantic context and stimulus quality on RT were observed, replicating previous work. In contrast, morphological context interacted with stimulus quality. This dissociation is discussed in the context of Besner and colleagues' evolving multistage framework. The essence of the account is that 1) stimulus quality affects feature and letter levels, but not later levels, 2) feedback from semantics to the lexical level is inoperative under low relatedness proportion conditions (hence stimulus quality and semantic context yield additive effects), whereas 3) feedback from the lexical level to the letter level is intact, hence stimulus quality and morphological context produce an interaction by virtue of them affecting a common stage of processing.     

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.     

Algebraic Semantics for Deductive Systems

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics.     

内涵与外延之辩:基于含糊性语义解释演进的分析

在含糊性问题研究领域,多值语义解释和超赋值语义解释是两个经典的研究进路。相较多值语义中的经典三值解释和基于概率赋值的模糊逻辑解释,范启德(1975)给出的超赋值语义由于引入了基于可能世界语义的可精确化结构,具有更强的表达力,能够弥补三值和模糊逻辑处理的很多不足。距离超赋值语义发表40余年后,秋叶研(2017)给出了同样满足可精确化结构条件的一个布尔多值解释。由于超赋值语义一直被当作典型的内涵语义处理方式,而在含糊性问题研究领域,布尔多值方法却在大多数时候被认为是模糊逻辑这个基于概率处理的典型的外延语义的复杂版本,内涵语义与外延语义的殊途同归,非常值得仔细思考和探究。本文将结合含糊性问题研究领域的多值语义解释和超赋值语义解释的演进过程,以内涵语义和外延语义的区分为切入点,最终指出,(当下主流定义下的)内涵语义与外延语义的界限是模糊的,而在原有界定基础上,对内涵语义增加“内涵语义要可以表达非线序的偏序结构”这一限制,能够进一步对内涵语义和外延语义进行区分。     

“Four-Valued” Semantics for the Relevant Logic R

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.     

Quantification over Sets of Possible Worlds in Branching-Time Semantics

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.     

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。     

The Refined Extension Principle for Semantics of Dynamic Logic Programming

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle the refined extension principle. Such principle is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.     

Truth-Maker Semantics for Intuitionistic Logic

I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.     

Reactive intuitionistic tableaux

We introduce reactive Kripke models for intuitionistic logic and show that the reactive semantics is stronger than the ordinary semantics. We develop Beth tableaux for the reactive semantics.     

Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information

We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.     

Semantical analysis of predicate logics without the contraction rule

In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.     

Indicative Conditionals and Graded Information

Journal of Philosophical Logic - I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics,...     

A Game Semantics for System P

In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is valid with respect to the game semantics if and only if it is valid with respect to the standard order semantics of System P. Combining these two results leads to a new completeness proof for System P with respect to its order semantics. Our approach allows us to construct for every inference either a concrete proof of the inference from the rules in System P or a countermodel in the order semantics. Our results rely on the notion of a witnessing set for an inference, whose existence is a concise, necessary and sufficient condition for validity of an inferences in System P. We also introduce an infinitary variant of System P and use the game semantics to show its completeness for the restricted class of well-founded orders.