• Combining Montague semantics and discourse representation
    Linguistics and Philosophy 19 (2). 1996.
    This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.
  • Type-Logical Semantics
    Routledge Encyclopedia of Philosophy Online. 2011.
    Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms…Read more
  • Categorial Grammar and Lexical-Functional Grammar
    In Miriam Butt & Tracey Holloway King (eds.), Proceedings of the LFG01 Conference, University of Hong Kong, Csli Publications. pp. 259-279. 2001.
    This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the metho…Read more
  • Perception Verbs
    In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics, Pergamon Press. pp. 6--2999. 1993.
    The semantics of a sentence containing a perception verb such as see or hear depends to a high degree on the exact syntactic form of the perception verb’s complement. Let us compare sentence (1), where the complement is tenseless, with (2), where the complement is a tensed clause
  • Sense and the computation of reference
    Linguistics and Philosophy 28 (4). 2004.
    The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of this relation must be given in the form…Read more
  • Order-independence and Underspecification
    In Hans Kamp & Barbara Hall Partee (eds.), Context-Dependence in the Analysis of Linguistic Meaning, Elsevier. pp. 11--239. 2004.
  • Existence predicate
    In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics, Pergamon. pp. 1191. 1993.
    Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject and a predicate, the underlying logical form, according to Russell, is the formula given in. This formula obviously has no subjectpredicate form and in fact ha…Read more
  • Lambda Grammars and the Syntax-Semantics Interface
    In Robert Van Rooij & Martin Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium, Illc. pp. 150-155. 2001.
    In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proof…Read more
  • Propositional Attitudes
    In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics, Pergamon Press. 1993.
    Verbs such as know, believe, hope, fear, regret and desire are commonly taken to express an attitude that one may bear towards a proposition and are therefore called verbs of propositional attitude. Thus in (1) below the agent Cathy is reported to have a certain attitude
  • Underspecified semantics
    In Klaus von Heusinger & Urs Egli (eds.), Reference and Anaphoric Relations, Kluwer Academic Publishers. pp. 311--338. 2000.
    Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating read…Read more
  • Higher Order Modal Logic
    In Patrick Blackburn, Johan Van Benthem & Frank Wolter (eds.), Handbook of Modal Logic, Elsevier. pp. 621-653. 2006.
    A logic is called higher order if it allows for quantification over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic began with Frege, was formalized in Russell [46] and Whitehead and Russell [52] early in the previous century, and received its canonical formulation in Church [14].1 While classical type theory has since long been overshadowed by set theory as a foundation of mathemat…Read more
  • An Analytic Tableau System for Natural Logic
    In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning, Springer. pp. 104-113. 2010.
    Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alterna…Read more
  • Talking about trees and truth-conditions
    Journal of Logic, Language and Information 10 (4): 417-455. 2001.
    We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical …Read more
  • In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.
  • Tense and the logic of change
    In Urs Egli, Peter Pause, Christoph Schwarze, Arnim von Stechow & Götz Wienold (eds.), Lexical Knowledge in the Organization of Language, John Benjamins. pp. 147-183. 1995.
    In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.
  • New directions in type-theoretic grammars
    Journal of Logic, Language and Information 19 (2): 129-136. 2010.
    This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a…Read more
  • Construction by Description in Discourse Representation
    with Noor van Leusen
    In Jaroslav Peregrin (ed.), Meaning: The Dynamic Turn, Elsevier. pp. 33-65. 2003.
    This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declarative…Read more
  • In this paper it is shown how a formal theory of interpretation in Montague’s style can be reconciled with a view on meaning as a social construct. We sketch a formal theory in which agents can have their own theory of interpretation and in which groups can have common theories of interpretation. Frege solved the problem how different persons can have access to the same proposition by placing the proposition in a Platonic realm, independent from all language users but accessible to all of them. …Read more
  • On Partial and Paraconsistent Logics
    Notre Dame Journal of Formal Logic 40 (3): 352-374. 1999.
    In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent …Read more
  • Intensional models for the theory of types
    Journal of Symbolic Logic 72 (1): 98-118. 2007.
    In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly,…Read more
  • Language, Lambdas, and Logic
    In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora (Studies in Linguistics and Philosophy 80), Kluwer Academic Publishers. pp. 23--54. 2003.
    The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.
  • A squib on anaphora and coindexing
    Linguistics and Philosophy 34 (1): 85-89. 2011.
    There are two kinds of semantic theories of anaphora. Some, such as Heim’s File Change Semantics, Groenendijk and Stokhof’s Dynamic Predicate Logic, or Muskens’ Compositional DRT (CDRT), seem to require full coindexing of anaphora and their antecedents prior to interpretation. Others, such as Kamp’s Discourse Representation Theory (DRT), do not require this coindexing and seem to have an important advantage here. In this squib I will sketch a procedure that the first group of theories may help t…Read more
  • This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim.
  • Program semantics and classical logic
    In CLAUS Report Nr 86, University of the Saarland. pp. 1-27. 1997).
    In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/}…Read more
  • Hyperfine-grained meanings in classical logic
    Logique Et Analyse 133 159-176. 1991.
    This paper develops a semantics for a fragment of English that is based on the idea of `impossible possible worlds'. This idea has earlier been formulated by authors such as Montague, Cresswell, Hintikka, and Rantala, but the present set-up shows how it can be formalized in a completely unproblematic logic---the ordinary classical theory of types. The theory is put to use in an account of propositional attitudes that is `hyperfine-grained', i.e. that does not suffer from the well-known problems …Read more
  • A relational formulation of the theory of types
    Linguistics and Philosophy 12 (3). 1989.
    This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.
  • Partial Information
    In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics, Pergamon Press. pp. 6--2952. 1993.
    the world of phenomena is immensely large this means we can perceive only part of the world. We see, feel and hear parts of reality, not the whole of it, and it seems that a sentence containing a verb of perception like 'John sees a house burn' is most naturally treated as saying that the subject sees an incomplete world in which the embedded sentence is true (see Barwise (1981) for this analysis). But if we want to analyse perception verbs thus, we must introduce some form of incompleteness int…Read more
  • The dynamics of discourse situations (extended abstract)
    with Massimo Poesio
    In Paul Dekker, Martin Stokhof & Yde Venema (eds.), Proceedings of the Eleventh Amsterdam Colloquium, University of Amsterdam. pp. 247-252. 1997.
    The effects of utterances such as cue phrases, keep-turn markers, and grounding signals cannot be characterized as changes to a shared record of the propositions under discussed: the simplest (and arguably most natural) way of characterizing the meaning of these utterances is in terms of a theory in which the conversational score is seen as a record of the discourse situation, or at least of the speech acts that have been performed. The problem then becomes to explain how discourse entities are …Read more
  • Analytic Tableaux for all of SIXTEEN_3
    with Stefan Wintein
    Journal of Philosophical Logic 44 (5): 473-487. 2015.
    In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require devel…Read more
  • Coreference
    In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics, Pergamon. pp. 769. 1993.
    In mathematical languages and in predicate logic coreferential terms can be interchanged in any sentence without altering the truth value of that sentence. Replacing 3 + 5 by 12 − 4 in any formula of arithmetic will never lead from truth to falsity or from falsity to truth. But natural languages are different in this respect. While in some contexts it is always allowed to interchange coreferential terms, other contexts do not admit this. An example of the first sort of context is likes bananas: …Read more