Constructive Analysis of Intensional Phenomena in Natural Language

2010

This book is, if you like, a snapshot of Transparent Intensional Logic as it looks in early 2010, and makes no claim to being the 'mature', let alone 'ultimate', statement of the theory. If the theory keeps evolving at its current pace, another update will be called for within the next 5-10 years. At the same time, a both methodological and philosophical constraint that is dear to us is that the applications we present should not be ad hoc. Rather they must fall out of an existing theory; and if a particular application calls for amendment of the foundations then it must be thoroughly justified. We like to think of Transparent Intensional Logic as an open-ended theory with a cast-iron core. The execution of the project informing Transparent Intensional Logic-a fully compositional procedural semantics applying indiscriminately to all logico-semantic contexts-is itself an open-ended process. 1 Writing this book together was fun. It was also rather a workout. Fun the way squash or handball is said to be fun, as Quine once commented after reading David Kaplan's 60-page paper 'Opacity'. We are indebted to a large group of people for stimulating discussions, advice, and encouragement, as well as to institutions for funding along the way. Among our favourite discussion partners are the Slovak logicians and philosophers helping develop TIL, notably Pavel Cmorej, František Gahér, Marián Zouhar and the Czech researchers Raclavský and Petr KuchyĖka, both using TIL to solve semantic problems. Moreover, we wish to thank several researchers who are familiar with or even well-versed in TIL without necessarily subscribing to the theory, including Gabriel Sandu, Andrew Holster, Jaroslav Peregrin, Vladimír Svoboda, Petr KoláĜ, Jan ŠtČpán and Vladimír Janák. Their questions and objections alerted us to problems which we might have otherwise neglected. It is also interesting to note that TIL⎯originally developed as a theory within philosophical logic⎯has turned out to be of particular interest to computer Preface ix JiĜí scientists, not least the members of a team led by Zdenko as well as some computer linguists, especially Aleš Horák. Marie Duží is grateful to her students Martina Nikola Ciprich, Michal Košinár, Marek Menšík, Jaroslav Müller, and the researchers involved in the Research Laboratory of Intelligent Systems (VSB-Technical University, Ostrava), whose comments contributed to the improvement of the text. Bjørn Jespersen would like to thank several of his colleagues at the Section of Philosophy at Delft University of Technology for their interest in Transparent Intensional Logic, not least Maarten Franssen. Finally, all three of us wish to thank two referees for Springer-Verlag for comments and recommendations that led us to reconsider and especially rephrase various portions of the book, not least the first two chapters. We also wish to thank Springer-Verlag for believing in the book, and Floor Oosting and Ingrid van Laarhoven for smooth handling.

The Language of Word Meaning, 2001

I would like to pose a set of fundamental questions regarding the constraints we can place on the structure of our concepts, particularly as revealed through language. I will outline a methodology for the construction of ontological types based on the dual concerns of capturing linguistic generalizations and satisfying metaphysical considerations. I discuss what "kinds of things" there are, as reflected in the models of semantics we adopt for our linguistic theories. I argue that the flat and relatively homogeneous typing models coming out of classic Montague Grammar are grossly inadequate to the task of modelling and describing language and its meaning. I outline aspects of a semantic theory (Generative Lexicon) employing a ranking of types. I distinguish first between natural (simple) types and functional types, and then motivate the use of complex types (dot objects) to model objects with multiple and interdependent denotations. This approach will be called the Principle of Type Ordering. I will explore what the top lattice structures are within this model, and how these constructions relate to more classic issues in syntactic mapping from meaning.

Journal of Logic, Language and Information, 2010

After a quick overview of the field of study known as "Lexical Semantics", where we advocate the need of accessing additional information besides syntax and Montaguestyle semantics at the lexical level in order to complete the full analysis of an utterance, we summarize the current formulations of a well-known theory of that field. We then propose and justify our own model of the Generative Lexicon Theory, based upon a variation of classical compositional semantics, and outline its formalization. Additionally, we discuss the theoretical place of informational, knowledge-related data supposed to exist within the lexicon as well as within discourse and other linguistic constructs.

2016

Modern Type Theories (MTTs) provide us with a new framework for formal semantics with attractive advantages as compared to Montague Grammar. First, MTTs have rich type structures that can be employed effectively to capture various linguistic features that have proved difficult in the Montagovian setting. Second, MTTs are prooftheoretically specified and can hence be usefully implemented in proof assistants such as Coq, where the MTT-semantics has been implemented for computer-assisted reasoning. These two respects may be characterised as saying that the MTT-semantics is both modeltheoretic and proof-theoretic. They offer unique features unavailable in traditional logical systems that have proved very useful in formal semantics. We shall introduce MTTs and how they can be used for formal semantics. The lectures will be informal and explanatory. They will be rigorous but contain a lot of examples, to illustrate the use of MTTs, on the one hand, and to compare the MTT-semantics with Mo...

Intensionality, the apparent failure of a normal referential interpretation of nominals in embedded positions, is a phenomenon that is pervasive in hu man language. It has been a foundational problem for semantics, defining a significant part of its agenda. Here we address the explanatory question of why it exists. Distinguishing lexical aspects of meaning from those that depend on grammatical patterning, we argue that intensionality is mainly grammatical in nature and origin: intensionality is an architectural consequence of the design of human grammar, although, in language use, lexical and pragmatic factors also play a role in the genesis of intuitions of nonsubstitutability salva veritate. Over the course of this paper, we offer a sequence of ten empirical arguments for this conclusion. A particular account of recursive structurebuilding in grammar is also offered, which predicts intensionality effects from constraints that govern how nominals of different grammatical types are embedded as arguments in larger units. Crucially, our account requires no appeal to a traditionally postu lated semantic ontology of 'senses' or 'thoughts' as entities 'denoted' by embed ded clauses, which, we argue, are explanatorily inert. It also covers intensionality characteristics in apparently nonsentential complements of verbs, which we further argue, against the claims of the recent 'Sententialist Hypothesis' , not to be sentential complements in disguise.

Tertium Non Datur, 1986

One of the primary aims of linguistic semantics is to translate the expressions of natural language into formulas of some logical calculus. These formulas, in turn, can be interpreted in the appropriate models, and semantic notions like truth, entailment, etc. can be formally defined in the usual manner. In addition to the well-known theoretical advantages of such an intermediate logical form, there is a practical advantage as well: given a system of rules for translation from formulas to natural language, it will be possible to translate from one natural language to another (via the interlingua) without actually evaluating the expressions of the source language. Although the calculi used as intermediate language in machine translation range from first-order predicate calculus (e.g. Schubert -Pelletier 1982) to the higher order intensional calculus of Montague Grammar (e.g. Landsbergen 1977), so far no type-free calculus has been employed for this purpose.

Principia: an international journal of epistemology, 2011

There are different ways we use the expressions "extension" and "intension". I specify in the first part of this paper two basic senses of this distinction, and try to show that the old metaphysical sense, by means of particular instance vs. universal, is more fundamental than the contemporary sense by means of substitutivity. In the second part, I argue that logic in general is essentially intensional, not only because logic is a rule-guided activity, but because even the extensional definition of a logic system presupposes an intensional notion of logical consequence.

1999

Journal of Logic, Language and Information, 2017

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

Arxiv preprint cmp-lg/9404010, 1994

Abstract: We present an analysis of the semantic interpretation of intensional verbs such as seek that allows them to take direct objects of either individual or quantifier type, producing both de dicto and de re readings in the quantifier case, all without needing to stipulate type-raising or quantifying-in rules. This simple account follows directly from our use of logical deduction in linear logic to express the relationship between syntactic structures and meanings. While our analysis resembles current categorial approaches in important ways, ...