First published in 1986, Knowledge, Belief, and Witchcraft remains the only analysis of indigenous discourse about an African belief system undertaken from within the framework of Anglo-American analytical philosophy. Taking as its point of departure W. V. O. Quine's thesis about the indeterminacy of translation, the book investigates questions of Yoruba epistemology and of how knowledge is conceived in an oral culture.

This textbook, which is completely self-contained and can be read by anyone with a secondary school education, is the result of the author's material prepared over the past 15 years of teaching introductory natural language semantics to graduate and undergraduate students at McGill University. The intended audience comprises undergraduate and graduate students in linguistics as well as those in philosophy, computer science and psychology with an interest in natural language semantics. The aim of the textbook is to teach (...) the fundamentals of natural language semantics, with English as the principal, though not the exclusive, target language. The principal aim of the textbook is to provide the student with all the basics necessary to be able him or her read research in natural language semantics, regardless of the theory assumed by the author of the research. In contrast to other textbooks in the field, which aim to introduce students to a particular theory of natural language semantics, this textbook seeks to give to its reader a clear overview of the kind of natural language phenomena which, at least prima facie, fall within the ambit of an investigation of natural language semantics; to assist the reader in developing a mastery of the mathematical tools used to formulate hypotheses about the natural language phenomena studied; and to impart to the reader an appreciation of the interplay between hypothesis and data. As a result, the textbook is rich in its presentation of the patterns of English, drawing extensively on the best and most contemporary descriptive grammars of English. The textbook also has more than 500 exercises, with answers to half of them. (shrink)

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a set of logical formulas—because a statement can be ambiguous, it can correspond to multiple formulas, (...) one for each reading. We argue that as long as we do not explicitly compute the interpretation in terms of possible world models, one can compute the semantic representation of a given statement, including aspects of lexical meaning. This is a very generic process, so the results are, at least in principle, widely applicable. We also discuss the algorithmic complexity of this process. (shrink)

This volume offers a general introduction to the field of semantics and provides coverage of the main perspectives.

I assume that the task of natural language semantics is to provide an unambiguous logical language into which natural language can be translated in such a way that the translating expressions display a structure which is isomorphic to the meaning of the translated expressions. Since language is a means of thinking and communicating mental contents, the meanings of singular terms cannot be the individuals of the substratist tradition, because such individuals are not cognizable entities. Thus I (...) propose that the logical language be based on Castaneda's guise theory, according to which singular terms always denote guises, i.e., roughly, bundles of properties. This, I argue, would result in a semantics which is in accordance with projects such as Lakoff's natural logic or Fodor's methodological solipsism. ;I first propose a formal system, GCC, which tries to be as faithful as possible to Castaneda's informal presentation of guise theory. It is therefore characterized by different forms of predication and a distinction between a level of property composition and a level of proposition composition. Such a distinction is dropped in a second system, GF, which presents a more traditional Fregean representation of predication. Yet, GF endorses essential assumptions of guise theory such as the existence of different sameness relations that can provide various interpretations for the English "is". I claim that GF provides more theoretical simplicity than GCC. ;Finally, I show the fruitfulness of the present approach by applying GF to a vast collection of linguistico-philosophical puzzles which includes but is not restricted to those that guise theory was originally designed to address: various versions of Frege's paradox, the paradox of analysis, Quine's puzzle on the number of planets, issues of reidentification and intentional identity, the anaphoric "it" of sentences such as "the lizard's tail fell off but then it grew back," problems connected with the use of "knowing-who ," proper names, indexicals and demonstratives. (shrink)

This paper examines the account of ordinary language semantics developed by Franz Brentano and his pupil Anton Marty. Long before the interest in ordinary language in the analytic tradition, Brentanian philosophers were exploring our everyday use of words, as opposed to the scientific use of language. Brentano and Marty were especially interested in the semantics of (common) names in ordinary language. They claimed that these names are vague, and that this is due to the structure of (...) the concepts that constitute their meaning: concepts expressed by such names are themselves vague, based on typicality, and have more or less similar items within their extension. After presenting the views of Brentano and Marty, this paper compares them to later accounts of meaning and concepts, notably Wittgenstein’s theory of family resemblances and the prototype theory of concepts, and emphasizes the originality of the Brentanian position. (shrink)

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality (...) presupposes that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

Paul M. Pietroski, University of Maryland I had heard it said that Chomsky’s conception of language is at odds with the truth-conditional program in semantics. Some of my friends said it so often that the point—or at least a point—finally sunk in.

In this paper, I shall provide a novel response to the argument from context-sensitivity against truth-conditional semantics. It is often argued that the contextual influences on truth-conditions outstrip the resources of standard truth-conditional accounts, and so truth-conditional semantics rests on a mistake. The argument assumes that truth-conditional semantics is legitimate if and only if natural language sentences have truth-conditions. I shall argue that this assumption is mistaken. Truth-conditional analyses should be viewed as idealised approximations of the complexities of natural (...) language meaning. From this perspective, disparity between the scientific model and its real-world target is to be expected. I elaborate on what such an approach to semantics would look like. (shrink)

Paul M. Pietroski, University of Maryland I had heard it said that Chomsky’s conception of language is at odds with the truth-conditional program in semantics. Some of my friends said it so often that the point—or at least a point—finally sunk in.

A BSTRACT. We present Property Theory with Curry Typing, an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types.1 We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most. We use the type system and our treatment of generalized quantifiers in natural language to construct a typetheoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous (...) type-theoretic analyses of this phenomenon. (shrink)

The contributions in this volume focus on the Bayesian interpretation of natural languages, which is widely used in areas of artificial intelligence, cognitive science, and computational linguistics. This is the first volume to take up topics in Bayesian Natural Language Interpretation and make proposals based on information theory, probability theory, and related fields. The methodologies offered here extend to the target semantic and pragmatic analyses of computational natural language interpretation. Bayesian approaches to natural language semantics and pragmatics (...) are based on methods from signal processing and the causal Bayesian models pioneered by especially Pearl. In signal processing, the Bayesian method finds the most probable interpretation by finding the one that maximizes the product of the prior probability and the likelihood of the interpretation. It thus stresses the importance of a production model for interpretation as in Grice’s contributions to pragmatics or in interpretation by abduction. (shrink)

This paper strives to characterize the relation between accent placement and discourse in terms of independent constraints operating at the interface between syntax and interpretation. The GIVENness Constraint requires un-F-marked constituents to be GIVEN. Key here is our definition of GIVENness which synthesizes insights from the literature on the semantics of focus with older views on information structure. AvoidF requires speakers to economize on F-marking. A third constraint requires a subset of F-markers to dominate accents.

Situation semantics was developed as an alternative to possible worlds semantics. In situation semantics, linguistic expressions are evaluated with respect to partial, rather than complete, worlds. There is no consensus about what situations are, just as there is no consensus about what possible worlds or events are. According to some, situations are structured entities consisting of relations and individuals standing in those relations. According to others, situations are particulars. In spite of unresolved foundational issues, the partiality provided by situation semantics (...) has led to some genuinely new approaches to a variety of phenomena in natural language semantics. In the way of illustration, this article includes relatively detailed overviews of a few selected areas where situation semantics has been successful: implicit quantifier domain restrictions, donkey pronouns, and exhaustive interpretations. It moreover addresses the question of how Davidsonian event semantics can be embedded in a semantics based on situations. Other areas where a situation semantics perspective has led to progress include attitude ascriptions, questions, tense, aspect, nominalizations, implicit arguments, point of view, counterfactual conditionals, and discourse relations. (shrink)

Independence Friendly Logic, introduced by Hintikka, is a logic in which a quantifier can be marked for being independent of other quantifiers. Dependence logic, introduced by Väänänen, is a logic with the complementary approach: for a quantifier it can be indicated on which quantifiers it depends. These logics are claimed to be useful for many phenomena, for instance natural language semantics. In this contribution we will compare these two logics by investigating their application in a compositional analysis of the (...) de dicto - de re ambiguity in natural language. It will be argued that Independence Friendly logic is suitable, whereas Dependence Logic is not. (shrink)

This paper describes a novel pedagogical software program that can be seen as an online companion to one of the standard textbooks of formal natural language semantics, Heim and Kratzer (1998). The Penn Lambda Calculator is a multifunctional application designed for use in standard graduate and undergraduate introductions to formal semantics: Teachers can use the application to demonstrate complex semantic derivations in the classroom and modify them interactively, and students can use it to work on problem sets provided by (...) the teacher. The program supports demonstrations and exercises in two main areas: (1) performing beta reduction in the simply typed lambda calculus; (2) application of the bottom-up algorithm for computing the compositional semantics of natural language syntax trees. The program is able to represent the full range of phenomena covered in the Heim and Kratzer textbook by function application, predicate modification, and lambda abstraction. This includes phenomena such as intersective adjectives, relative clauses and quantifier raising. In the student use case, emphasis has been placed on providing “live” feedback for incorrect answers. Heuristics are used to detect the most frequent student errors and to return specific, interactive suggestions. (shrink)

For most of the 1980s, Jon Barwise focused much of his research in the area of natural language semantics. This article surveys his research publications in that area.Most, but not all, of those publications were in the area of situation semantics, a new approach to natural language semantics Barwise developed jointly with his colleague John Perry in the first half of the 1980s. That work was both blessed, and cursed, by becoming closely identified in academic circles with the (...) award of a $23 million gift to Stanford from the System Development Foundation for the establishment in 1983 of its Center for the Study of Language and Information. The development of situation semantics, and in due course its underlying mathematical foundation Situation Theory, carried out for the most part within the framework of CSLI's STASS research group, was actually a relatively small part of the overall research program at CSLI. But because Barwise and Perry were leading figures at CSLI, were centrally involved in securing the SDF gift, and were respectively the first and second directors of CSLI, a general impression sprung up that the two of them had been awarded millions of dollars to develop situation semantics.A major consequence of this false impression was that from the theory's early days, a great deal of interest was shown in the project. With so many accomplished scholars pouring over the work while the ink was still wet on the manuscript pages, Barwise and Perry were able to take advantage of a broad range of helpful criticism. This meant that they were able to develop the new theory much more rapidly than would otherwise have been the case. (shrink)

Transparent intensional logic (TIL) is a well-explored type-theoretical framework for semantics of natural language. However, its treatment of polymorphic functions, which are essential for the analysis of various natural language phenomena, is still underdeveloped. In this paper, we address this issue and propose an extension of TIL that introduces polymorphism via type variables ranging over types and generalized variables ranging over constructions and types. Furthermore, we offer an analysis of sentences involving non-specific notional attitudes of the general form (...) ‘_A_ considers (believes, desires, wants, seeks,...) something’. (shrink)

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various roles (...) in conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology. (shrink)

This book develops a theory of enriched meanings for natural language interpretation that uses the concept of monads and related ideas from category theory. The volume is interdisciplinary in nature, and will appeal to graduate students and researchers from a range of disciplines interested in natural language understanding and representation.

By creating certain marks on paper, or by making certain sounds-breathing past a moving tongue-or by articulation of hands and bodies, language users can give expression to their mental lives. With language we command, assert, query, emote, insult, and inspire. Language has meaning. This fact can be quite mystifying, yet a science of linguistic meaning-semantics-has emerged at the intersection of a variety of disciplines: philosophy, linguistics, computer science, and psychology. Semantics is the study of meaning. But what (...) exactly is "meaning"? What is the exact target of semantic theory? Much of the early work in natural language semantics was accompanied by extensive reflection on the aims of semantic theory, and the form a theory must take to meet those aims. But this meta-theoretical reflection has not kept pace with recent theoretical innovations. This volume re-addresses these questions concerning the foundations of natural language semantics in light of the current state-of-the-art in semantic theorising. (shrink)

Mandarin Chinese, along with Japanese, Yorùbá, Mòoré, and Samoan, has been argued to lack ‘degree abstraction’, a configuration at LF involving lambda abstraction over a degree variable. These languages are claimed to have a negative setting for a hypothesized ‘Degree Abstraction Parameter’. Recent work, however, has argued for degree abstraction in Japanese and Yorùbá, and degree abstraction has been detected in a number of additional languages. Could it in fact be universal? Here, we focus on the case of Mandarin, and (...) argue that Mandarin has degree abstraction too. We offer three arguments in favor of degree abstraction in Mandarin, based on attributive comparatives, comparatives with embedded predicates, and scope interactions with modals. We also rebut prior arguments for the lack of degree abstraction in Mandarin, considering degree questions, measure phrases, and negative island effects. Taken together, these results show that degree abstraction is not a parameter along which Mandarin and English vary, and suggest rather that degree abstraction may be universally available. (shrink)

In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and 1970s, Montague himself didn't make (...) use of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question. (shrink)

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like “most.” We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic (...) analyses of this phenomenon. (shrink)

This paper argues for the philosophical and semantic importance of attitudinal objects, entities such as judgments, claims, beliefs, demands, and desires, as an ontological category distinct from that of events and states and from that of propositions. The paper presents significant revisions and refinements of the notion of an attitudinal object as it was developed in my previous work.

In this paper, we show that Higher{Order Coloured Uni cation { a form of uni cation developed for automated theorem proving { provides a general theory for modeling the interface between the interpretation process and other sources of linguistic, non semantic information. In particular, it provides the general theory for the Primary Occurrence Restriction which (Dalrymple et al., 1991)'s analysis called for.

Jody Azzouni argues that we involuntarily experience certain physical items, certain products of human actions, and certain human actions themselves as having meaning-properties. We understand these items as possessing meaning or as having truth values. For example, a sign on a door reading "Drinks Inside" strikes native English speakers as referring to liquids in the room behind the door. The sign has a truth value--if no drinks are found in the room, the sign is misleading. Someone pointing in a direction (...) has the same effect: we experience her gesture as significant. Azzouni does not suggest that we don't recognize the expectations or intentions of speakers ; we do recognize that the person pointing in a certain direction intends for us to understand her gesture's significance. Nevertheless, Azzouni asserts that we experience that gesture as having significance independent of her intentions. The gesture is meaningful on its own. The same is true of language, both spoken and written. We experience the meanings of language artifacts as independent of their makers' intentions in the same way that we experience an object's shape as a property independent of the object's color. There is a distinctive phenomenology to the experience of understanding language, and Semantic Perception shows how this phenomenology can be brought to bear as evidence for and against competing theories of language. (shrink)

We develop a framework for natural language semantics which handles intensionality via metalogical constructions and deals with degree truth values in an integrated way. We take an axiomatic set theory, ZF, as the foundation for semantic representations, but we make ZF a metalanguage for part of itself by embedding a language ℒ within ZF which is basically a copy of the part of ZF consisting of set expressions. This metalogical set-up is used for handling propositional attitude verbs (limited (...) to believe in this paper). We define a truth function τ which determines the truth value τ(p, T) of an ℒ-proposition p with respect to a theory T. Theories are sets of ℒ-propositions with associated truth values, and can be viewed as a (much more well-defined) replacement for possible worlds. We develop a mechanism for defining belief worlds as theories. We simultaneously develop two different versions of our system - a Boolean version where the set Ω of truth values is {0, 1}, and a degree-truth version where Ω is the interval [0, 1] of real numbers. We use degrees of truth in handling a broad class of semantic predicates that we call base-focus predicates, which include generalized quantifiers as well as many adverb and adjective senses and certain discourse-level predicates. (shrink)

This extended investigation of the semantics of event (and state) sentences in their various forms is a major contribution to the semantics of natural language, simultaneously encompassing important issues in linguistics, philosophy, and logic. It develops the view that the logical forms of simple English sentences typically contain quantification over events or states and shows how this view can account for a wide variety of semantic phenomena. Focusing on the structure of meaning in English sentences at a &"subatomic&" level&-that (...) is, a level below the one most theories accept as basic or &"atomic&"&-Parsons asserts that the semantics of simple English sentences require logical forms somewhat more complex than is normally assumed in natural language semantics. His articulation of underlying event theory explains a wide variety of apparently diverse semantic characteristics of natural language, and his development of the theory shows the importance of seeing the distinction between events and states. Parsons demonstrates that verbs, also, indicate kinds of actions rather than specific, individual actions. Verb phrases, too, he argues, depend on modifiers to make their function and meaning in a sentence specific. An appendix gives many of the details needed to formalize the theory discussed in the body of the text and provides a series of templates that permit the generation of atomic formulas of English. (shrink)

The paper presents Property Theory with Curry Typing where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides a useful analysis of conjunctive terms. (...) Such terms can be given a single polymorphic type that expresses the fact that they can conjoin phrases of any one type, yielding an expression of the same type. (shrink)