Making computational sense of Montague's intensional logic

Montague's difficult notation and complex model theory have tended to obscure potential insights for the computer scientist studying Natural Language. Despite his strict insistence on an abstract model-theoretic interpretation for his formalism, we feel that Montague's work can be related to procedural semantics in a fairly direct way. A simplified version of Montague's formalism is presented, and its key concepts are explicated in terms of computational analogues. Several examples are presented within Montague's formalism but with a view toward developing a procedural interpretation. We provide a natural translation from intensional logic into lisp. This allows one to express the composition of meaning in much the way Montague does, using subtle patterns of functional application to distribute the meanings of individual words throughout a sentence. The paper discusses some of the insights this research has yielded on knowledge representation and suggests some new ways of looking at intensionality, context, and expectation.     

THE ARCHITECTURE OF SYSTEMS PROBLEM SOLVING by George J. Klir. Plenum Press,New York, 1985, xvi + 540 pages.

This is an overview paper presenting the main results obtained by the author and his colleagues in the field of fuzzy logic and modelling of natural language semantics and is composed of an introduction followed by two main parts. Section 2 discusses our results in terms of fuzzy logic, namely that of prepositional and first-order fuzzy logic based on a residuated lattice of truth values. Section 3 presents the concept of the Alternative mathematical Model of natural Language semantics and pragmatics (AML) the development of which is based on a philosophical approach rather than the approaches usually adopted in most classical papers.     

Adjectival and Adverbial Modification: The View from Modern Type Theories

In this paper we present a study of adjectival/adverbial modification using modern type theories (MTTs), i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented (e.g. in proof-assistants) given their proof-theoretic nature. In MTT-semantics, common nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate mechanism to model these cases. In particular, this modelling naturally takes care of the characterising inferences associated with each class of adjectives. Then, more advanced issues on adjectival modification are discussed: (a) degree adjectives, (b) comparatives and (c) multidimensional adjectives. There, it is shown that the use of indexed types can be usefully applied in order to deal with these cases. In the same vein, the issue of adverbial modification is discussed. We study two general typings for sentence and VP adverbs respectively. It is shown that the rich type structure in MTTs further provides useful organisational mechanisms in giving formal semantics for adverbs. In particular, we discuss the use of \(\varSigma \)-types to capture the veridicality/non-veridicality distinction and further discuss cases of intensional adverbs using the type theoretic notion of context (i.e. without resorting to intensional typing). We also look at manner, subject and speech act adverbials and propose solutions using MTTs. Finally, we show that the current proof technology can help mechanically check the associated inferences. A number of our proposals concerning adjectival and adverbial modification have been formalised in the proof assistant Coq and many of the associated inference patterns are checked to be correctly captured.     

Shifting semantic values of English phrases for classification

The researches of semantics (positive, negative, neutral) are performed for a long time and they are very important for many commercial applications, many scientific works, etc. In this paper we propose a new model to calculate the emotional values (or semantic scores) of English terms (English verbs, English nouns, English adjectives, English adverbs, etc.) as follows: firstly, we create our basis English emotional dictionary (called bEED) by using Sorensen measure (Sorensen coefficient, called SM) through Google search engine with AND operator and OR operator and secondly, many English adjective phrases, English adverb phrases and English verb phrases are created based on the English grammars (the English characteristics) by combining the English adverbs of degree with the English adjectives, the English adverbs and English verbs; finally, the valences of the English adverb phrases are identified by their specific contexts. The English phrases often bring the semantics which the values (or emotional scores) are not fixed and are changed when they appear in their different contexts. Therefore, the results of the sentiment classification are not high accuracy if the English phrases bring the emotions and their semantic values (or their sentiment scores) are not changed in any context. For those reasons, we propose many rules based on English language grammars to calculate the sentimental values of the English phrases bearing emotion in their specific contexts. The results of this work are widely used in applications and researches of the English semantic classification.     

An empirical study of representing adjectives over knowledge bases: Approach,lexicon and application

Adjectives are common in natural language, and their usage and semantics have been studied broadly. In recent years, with the rapid growth of knowledge bases (KBs), many knowledge-based question answering (KBQA) systems are developed to answer users’ natural language questions over KBs. A fundamental task of such systems is to transform natural language questions into structural queries, e.g., SPARQL queries. Thus, such systems require knowledge about how natural language expressions are represented in KBs, including adjectives. In this paper, we specifically address the problem of representing adjectives over KBs. We propose a novel approach, called Adj2SP, to represent adjectives as SPARQL query patterns. Adj2SP contains a statistic-based approach and a neural network-based approach, both of them can effectively reduce the search space for adjective representations and overcome the lexical gap between input adjectives and their target representations. Two adjective representation datasets are built for evaluation, with adjectives used in QALD and Yahoo! Answers, as well as their representations over DBpedia. Experimental results show that Adj2SP can generate representations of high quality and significantly outperform several alternative approaches in F1-score. Furthermore, we publish Lark, a lexicon for adjective representations over KBs. Current KBQA systems show an improvement of over 24% in F1-score by integrating Adj2SP.     

面向信息处理的语境形式化研究

在自然语言处理研究领域中,句法研究已经取得了可喜的进展,语义研究也日益受到重视。但要真正实现计算机理解自然语言的目标,还必须进一步深入开展语用分析研究,目前还很少有这方面的研究成果。语境是语用学研究中的重要内容,本文首先讨论了现代语言学关于语境的定义,对计算语言学中的语境作了科学的界定,然后给出了语境及其相关概念的形式定义,并结合汉语实例进行了分析。最后指出“计算语用学”这一计算语言学领域中的新兴学科将大有可为。     

The Use of Situation Theory in Context Modeling

At the heart of natural language processing is the understanding of context dependent meanings. This paper presents a preliminary model of formal contexts based on situation theory. It also gives a worked‐out example to show the use of contexts in lifting, i.e., how propositions holding in a particular context transform when they are moved to another context. This is useful in NLP applications where preserving meaning is a desideratum.     

Toward a computational interpretation of situation semantics1

Situation semantics proposes novel and attractive treatments for several problem areas of natural language semantics, such as efficiency (context sensitivity) and prepositional attitude reports. Its focus on the information carried by utterances makes the approach very promising for accounting for pragmatic phenomena. However, situation semantics seems to oppose several basic assumptions underlying current approaches to natural language processing and the design of intelligent systems in general. It claims that efficiency undermines the standard notions of logical form, entailment, and proof theory, and objects to the view that mental processes necessarily involve internal representations. The paper attempts to clarify these issues and discusses the impact of situation semantics’ criticisms for natural language processing, knowledge representation, and reasoning. I claim that the representational approach is the only currently practical one for the design of large intelligent systems, but argue that the representations used should be efficient in order to account for the system's embedding in its environment. The paper concludes by stating some constraints that a computational interpretation of situation semantics should obey and discussing remaining problems.     

Natural Language Inference in Coq

In this paper we propose a way to deal with natural language inference (NLI) by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory (MTT) with coercive subtyping as the formal language into which we translate natural language semantics, and we further implement these semantics in the Coq proof assistant. It is shown that the use of a MTT with an adequate subtyping mechanism can give us a number of promising results as regards NLI. Specifically, it is shown that a number of inference cases, i.e. quantifiers, adjectives, conjoined noun phrases and temporal reference among other things can be successfully dealt with. It is then shown, that even though Coq is an interactive and not an automated theorem prover, automation of all of the test examples is possible by introducing user-defined automated tactics. Lastly, the paper offers a number of innovative approaches to NL phenomena like adjectives, collective predication, comparatives and factive verbs among other things, contributing in this respect to the theoretical study of formal semantics using MTTs.     

An Ontology-Based Approach to Metaphor Cognitive Computation

Language understanding is one of the most important characteristics for human beings. As a pervasive phenomenon in natural language, metaphor is not only an essential thinking approach, but also an ingredient in human conceptual system. Many of our ways of thinking and experiences are virtually represented metaphorically. With the development of the cognitive research on metaphor, it is urgent to formulate a computational model for metaphor understanding based on the cognitive mechanism, especially with the view to promoting natural language understanding. Many works have been done in pragmatics and cognitive linguistics, especially the discussions on metaphor understanding process in pragmatics and metaphor mapping representation in cognitive linguistics. In this paper, a theoretical framework for metaphor understanding based on the embodied mechanism of concept inquiry is proposed. Based on this framework, ontology is introduced as the knowledge representation method in metaphor understanding, and metaphor mapping is formulated as ontology mapping. In line with the conceptual blending theory, a revised conceptual blending framework is presented by adding a lexical ontology and context as the fifth mental space, and a metaphor mapping algorithm is proposed.     

信息语义学：一个新计算语义学的构想

我们的目的是探索一个新的计算语义学理论——信息语义学,本文大体勾勒出它的总体构,论述其基础,即基本概念,基本假设,基本原理.     

Effective Diagrammatic Communication: Syntactic,Semantic and Pragmatic Issues

The study of systems of communication may be divided into three parts: syntax, semantics and pragmatics. Accounts of the embedding of text-based languages in the computational processes of reasoners and communicators are relatively well developed, with accounts available for a spectrum of languages ranging from the highly formalised and constrained, such as formal logics, to the highly informal and unconstrained natural languages used in everyday conversations. Analogies between diagrams and such textual representations of information are quite revealing about similarities and differences and can provide a useful starting point for exploring the issues in a theory of diagrammatic communication.This paper sketches out a theory of diagrammatic communication, based upon recent studies of the syntactic, semantic and pragmatic component issues which such a theory must accommodate. In the context of this theory an exploration is made of the issues involved in answering the question: what makes for an effective diagrammatic representation? To achieve this we review a framework in which we may explore properties of representations, and properties of the relation between representations and that which they represent. By relating this framework to our sketched theory of diagrammatic communication, we explore the concept of effectiveness in diagrams. This process of exploration enables us to relate previous studies of the effectiveness of diagrams into a broader, unified framework, which clarifies both the various issues relating to effectiveness and the relations between them.     

A framework for linguistic logic programming

Lawry's label semantics for modeling and computing with linguistic information in natural language provides a clear interpretation of linguistic expressions and thus a transparent model for real‐world applications. Meanwhile, annotated logic programs (ALPs) and its fuzzy extension AFLPs have been developed as an extension of classical logic programs offering a powerful computational framework for handling uncertain and imprecise data within logic programs. This paper proposes annotated linguistic logic programs (ALLPs) that embed Lawry's label semantics into the ALP/AFLP syntax, providing a linguistic logic programming formalism for development of automated reasoning systems involving soft data as vague and imprecise concepts occurring frequently in natural language. The syntax of ALLPs is introduced, and their declarative semantics is studied. The ALLP SLD‐style proof procedure is then defined and proved to be sound and complete with respect to the declarative semantics of ALLPs. © 2010 Wiley Periodicals, Inc.     

A Rewriting Logic Approach to Operational Semantics (Extended Abstract)

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuation-based semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

A rewriting logic approach to operational semantics

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, continuation-based semantics, and the chemical abstract machine. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Intensional and Extensional Semantics of Dataflow Programs

We compare two semantic models of dataflow programs: a synchronous version of the classical Kahn semantics, and a new semantics in a category of synchronous processes. We consider the Kahn semantics to be extensional, as it describes the functions computed by dataflow nodes, and the categorical semantics to be intensional, as it describes the step-by-step production of output tokens from input tokens. Assuming that programs satisfy Wadges cycle sum condition and are therefore deadlock-free, we prove that the two semantics are equivalent. This equivalence result amounts to a proof that function composition in the extensional semantics is faithfully modelled by the detailed interactions of the intensional semantics, and provides further insight into the nature of dataflow computation.     

Verification of programs that destructively manipulate data

We investigate various equivalence relations between expressions in a first-order functional programming language augmented with the ability to destructively alter the underlying data. To define the semantics we introduce the notion of a memory structure. A computation theory for lexically scoped functional language is then defined over these structures. The equivalence relations are then defined within this model theoretic framework. A distinction is made between intensional relations and extensional relations. The former class turn out to have a much more manageable theory than the latter. The principal intensional relation studied is strong isomorphism, its properties allow for elegant verification proofs in a style similar to that of purely applicative languages. In particular the relation is preserved under many standard syntactic manipulations and transformations.     

自然语言处理中的逻辑词

词是自然语言处理中最基本的单位,在当今知识表示领域,知识图作为自然语言理解的语义模型有其独到之处。本文从语言学和逻辑学的角度,首次提出并探讨了逻辑词研究逻辑词分类及如何用知识图表示各类逻辑词的结构。对自然语言处理中研究复句和篇章的理解提供了一种新的途径。