Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.     

Many Concepts and Two Logics of Algorithmic Reduction

Within the program of finding axiomatizations for various parts of computability logic, it was proven earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting’s intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algorithmic reduction, however, is the one that does not allow such reusage. The present article shows that turning the logic of the first sort of reduction into the logic of the second sort of reduction takes nothing more than just deleting the contraction rule from its Gentzen-style axiomatization. The first (Turing) sort of interactive reduction is also shown to come in three natural versions. While those three versions are very different from each other, their logical behaviors (in isolation) turn out to be indistinguishable, with that common behavior being precisely captured by implicative intuitionistic logic. Among the other contributions of the present article is an informal introduction of a series of new — finite and bounded — versions of recurrence operations and the associated reduction operations. Presented by Robert Goldblatt     

Predicate Logical Extensions of some Subintuitionistic Logics

The paper presents predicate logical extensions of some subintuitionistic logics. Subintuitionistic logics result if conditions of the accessibility relation in Kripke models for intuitionistic logic are dropped. The accessibility relation which interprets implication in models for the propositional base subintuitionistic logic considered here is neither persistent on atoms, nor reflexive, nor transitive. Strongly complete predicate logical extensions are modeled with a second accessibility relation, which is a partial order, for the interpretation of the universal quantifier. Presented by Melvin Fitting     

A semantics-based approach to the "no negative evidence" problem

Previous studies have shown that children retreat from argument-structure overgeneralization errors (e.g., * Don't giggle me ) by inferring that frequently encountered verbs are unlikely to be grammatical in unattested constructions, and by making use of syntax-semantics correspondences (e.g., verbs denoting internally caused actions such as giggling cannot normally be used causatively). The present study tested a new account based on a unitary learning mechanism that combines both of these processes. Seventy-two participants (ages 5–6, 9–10, and adults) rated overgeneralization errors with higher (* The funny man's joke giggled Bart ) and lower (* The funny man giggled Bart ) degrees of direct external causation. The errors with more-direct causation were rated as less unacceptable than those with less-direct causation. This finding is consistent with the new account, under which children acquire—in an incremental and probabilistic fashion—the meaning of particular constructions (e.g., transitive causative = direct external causation) and particular verbs, rejecting generalizations where the incompatibility between the two is too great.     

Studies on time: a proposal on how to get out of circularity

The analysis of time is vitiated very often by circularity: several disciplines, such as psychology, linguistics, and neurosciences, analyze time by using concepts or terms which already contain in themselves, or are based, on the experience and notion of time (as when, for example, time is defined as “duration”, or when our ability to estimate durations is explained by resorting to the notion of an internal clock). Some detailed examples of circularity in the analysis of time are given here and examined. A way out of circularity is then given: it is represented by the proposal of attentional semantics (AS) of considering words and their meanings in terms of the aim they serve, and the means and processes developed and implemented in order to achieve that aim. According to AS, the main aim of words is that of indicating to, and eliciting in, the listener or reader a specific conscious experience: namely, the conscious experience referred to by their meanings. Words achieve their main aim by conveying the condensed instructions on the attentional operations one has to perform if one wants to consciously experience what is expressed through and by them. By describing the conscious experiences elicited by words in terms of the attentional operations that are responsible for the production of such conscious experiences, AS offers an a-linguistic counterpart to language, and therefore an effective way out of circularity. Following in footsteps of Mach (Contributions to the analysis of the sensations, 1890), but slightly revising his hypothesis, AS defines time-sensation as the perception of the effort made, or alternatively the nervous energy expended, by the organ of attention when performing a “temporal activity” (for instance, estimating duration), that is, when one’s own attention is focused in a continuous and incremental way on the conscious product of the (“non-temporal”) activity performed by means of another portion of one’s attention.

Combinatory Logic and the Semantics of Substructural Logics

The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms to the basic positive relevant logic B∘T, then LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself. Presented by Rob Goldblatt     

The Wind Chilled the Spectators, but the Wine Just Chilled: Sense, Structure, and Sentence Comprehension

Anticipation plays a role in language comprehension. In this article, we explore the extent to which verb sense influences expectations about upcoming structure. We focus on change of state verbs like shatter , which have different senses that are expressed in either transitive or intransitive structures, depending on the sense that is used. In two experiments we influence the interpretation of verb sense by manipulating the thematic fit of the grammatical subject as cause or affected entity for the verb, and test whether readers' expectations for a transitive or intransitive structure change as a result. This sense-biasing context influenced reading times in the postverbal regions. Reading times for transitive sentences were faster following good-cause than good-theme subjects, but the opposite pattern was found for intransitive sentences. We conclude that readers use sense-contingent subcategorization preferences during on-line comprehension.     

基于语义的词汇判断的计算模型

词汇判断是一种在字词认知研究中广泛使用的实验范式。本文提出了一个基于分布式语义表征的计算模型,用来解释某些在词汇判断作业中出现的实验现象。模型是一个包括词形层、隐层、语义层、词典层和判断层的前传网络。词形层、隐层和语义层之间的连接权重在学习过程中被不断调整,使用反传算法进行学习。语义层、词典层和判断层之间的连接权重在学习前就已被固定,在学习过程中不进行调整。模型模拟了在词汇判断作业中出现的四种实验现象：（１）频率效应;（２）语义启动效应;（３）频率与语境的交互作用;（４）重复启动效应。模型所表现出的行为特性由模型的框架和学习算法所决定。