Knowledge on Treelike Spaces

This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system.     

More Triviality

This paper uses the framework of Popper and Miller's work on axiom systems for conditional probabilities to explore Adams' thesis concerning the probabilities of conditionals. It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it.     

Semantics, conceptual spaces, and the meeting of minds

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions.     

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.     

Some topological properties of paraconsistent models

In this work, we investigate the relationship between paraconsistent semantics and some well-known topological spaces such as connected and continuous spaces. We also discuss homotopies as truth preserving operations in paraconsistent topological models.     

The influence of consistency, frequency, and semantics on learning to read: an artificial orthography paradigm

Two experiments explored learning, generalization, and the influence of semantics on orthographic processing in an artificial language. In Experiment 1, 16 adults learned to read 36 novel words written in novel characters. Posttraining, participants discriminated trained from untrained items and generalized to novel items, demonstrating extraction of individual character sounds. Frequency and consistency effects in learning and generalization showed that participants were sensitive to the statistics of their learning environment. In Experiment 2, 32 participants were preexposed to the sounds of all items (lexical phonology) and to novel definitions for half of these items (semantics). Preexposure to either lexical phonology or semantics boosted the early stages of orthographic learning relative to Experiment 1. By the end of training, facilitation was restricted to the semantic condition and to items containing low-frequency inconsistent vowels. Preexposure reduced generalization, suggesting that enhanced item-specific learning was achieved at the expense of character-sound abstraction. The authors' novel paradigm provides a new tool to explore orthographic learning. Although the present findings support the idea that semantic knowledge supports word reading processes, they also suggest that item-specific phonological knowledge is important in the early stages of learning to read.     

Occasioned Semantics: A Systematic Approach to Meaning in Talk

This paper puts forward an argument for a systematic, technical approach to formulation in verbal interaction. I see this as a kind of expansion of Sacks’ membership categorization analysis, and as something that is not offered (at least not in a fully developed form) by sequential analysis, the currently dominant form of conversation analysis. In particular, I suggest a technique for the study of “occasioned semantics,” that is, the study of structures of meaningful expressions in actual occasions of conversation. I propose that meaning and rhetoric be approached through consideration of various dimensions or operations or properties, including, but not limited to, contrast and co-categorization, generalization and specification, scaling, and marking. As illustration, I consider a variety of cases, focused on generalization and specification. The paper can be seen as a return to some classical concerns with meaning, as illuminated by more recent insights into indexicality, social action, and interaction in recorded talk.     

Probabilistic argumentation systems: A new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster–Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.     

Quantified extensions of canonical propositional intermediate logics

The quantified extension of a canonical prepositional intermediate logic is complete with respect to the generalization of Kripke semantics taking into consideration set-valued functors defined on a category.     

Acquiring and processing verb argument structure: distributional learning in a miniature language

Adult knowledge of a language involves correctly balancing lexically-based and more language-general patterns. For example, verb argument structures may sometimes readily generalize to new verbs, yet with particular verbs may resist generalization. From the perspective of acquisition, this creates significant learnability problems, with some researchers claiming a crucial role for verb semantics in the determination of when generalization may and may not occur. Similarly, there has been debate regarding how verb-specific and more generalized constraints interact in sentence processing and on the role of semantics in this process. The current work explores these issues using artificial language learning. In three experiments using languages without semantic cues to verb distribution, we demonstrate that learners can acquire both verb-specific and verb-general patterns, based on distributional information in the linguistic input regarding each of the verbs as well as across the language as a whole. As with natural languages, these factors are shown to affect production, judgments and real-time processing. We demonstrate that learners apply a rational procedure in determining their usage of these different input statistics and conclude by suggesting that a Bayesian perspective on statistical learning may be an appropriate framework for capturing our findings.     

A semantical investigation on Brouwer-Zadeh logic

Conclusion In the standard approach to quantum mechanics, closed subspaces of a Hilbert space represent propositions. In the operational approach, closed subspaces are replaced by effects that represent a mathematical counterpart for properties which can be measured in a physical system. Effects are a proper generalization of closed subspaces. Effects determine a Brouwer-Zadeh poset which is not a lattice. However, such a poset can be embedded in a complete Brouwer-Zadeh lattice. From an intuitive point of view, one can say that these structures represent a natural logical abstraction from the structure of propositions of a quantum system. The logic that arises in this way is Brouwer-Zadeh logic. This paper shows that such a logic can be characterized by means of an algebraic and a Kripkean semantics. Finally, a strong completeness theorem for BZL is proved.     

Axiomatizing the Logic of Imagination

In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed system. In the present paper I offer a solution to this problem by providing a complete axiomatization of a generalization of the original semantics. The difficulty in proving completeness lies in the fact that the modalities that capture the notion of truth in an act of imagination are neither standard nor minimal, so that the construction of the canonical model and the proof of the truth lemma are to be substantially modified.

     

On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.     

Semantic embodiment,disembodiment or misembodiment? In search of meaning in modules and neuron circuits

“Embodied” proposals claim that the meaning of at least some words, concepts and constructions is grounded in knowledge about actions and objects. An alternative “disembodied” position locates semantics in a symbolic system functionally detached from sensorimotor modules. This latter view is not tenable theoretically and has been empirically falsified by neuroscience research. A minimally-embodied approach now claims that action–perception systems may “color”, but not represent, meaning; however, such minimal embodiment (misembodiment?) still fails to explain why action and perception systems exert causal effects on the processing of symbols from specific semantic classes. Action perception theory (APT) offers neurobiological mechanisms for “embodied” referential, affective and action semantics along with “disembodied” mechanisms of semantic abstraction, generalization and symbol combination, which draw upon multimodal brain systems. In this sense, APT suggests integrative-neuromechanistic explanations of why both sensorimotor and multimodal areas of the human brain differentially contribute to specific facets of meaning and concepts.     

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。     

Pseudo-Boolean valued prolog

A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.Research supported by PSC-CUNY Grants 666396, 667295 and NSF Grant CCR-8702307.