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Reinhard Muskens [39]Reinhard Anton Muskens [1]
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Profile: Reinhard Muskens (Tilburg University)
  1. Reinhard Muskens, An Analytic Tableau System for Natural Logic.
    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 alternative approach (...)
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  2. Reinhard Muskens, Logical Omniscience.
    Let us call two expressions synonymous if and only if they may be interchanged in each sentence without altering the truth value of that sentence.' With the help of an argument by Benson Mates (Mates [1950j) it can be..
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  3. Reinhard Muskens, Type-Logical Semantics.
    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 (...)
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  4. Reinhard Muskens, Construction by Description in Discourse Representation.
    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 declaratively if logic is used (...)
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  5. Reinhard Muskens, Categorial Grammar and Lexical-Functional Grammar.
    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 method seems more practicable.
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  6. Reinhard Muskens, Description Theory, LTAGs and Underspecified Semantics.
    underspecified syntactic representation and its com- Descriptions in our theory model three kinds of inpletions is to let the underspecified representation formation. First, there are input descriptions, which correspond to a logical description and the comple-.
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  7. Reinhard Muskens, Exploring Logical Dynamics, Door Johan Van Benthem.
    Veel Nederlandse woorden (dans, zet, oordeel, assertie, ...) duiden zowel een handeling aan als het resultaat van die handeling. Het fenomeen doet zich in vrijwel alle talen voor en het lijkt erop dat het menselijke cognitieve apparaat er niet zoveel moeite mee heeft te wisselen tussen een statisch perspectief dat resultaten ziet en een dynamisch perspectief dat vooral gericht is op de processen die tot die resultaten geleid hebben. De filosofie heeft meer moeite met het wisselen tussen een statisch en (...)
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  8. Reinhard Muskens, Existence Predicate.
    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 (the noun phrase ‘the king of France’) and a predicate (the verb phrase ‘exists’), the underlying logical form, according (...)
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  9. Reinhard Muskens, Λ-Grammars and the Syntax-Semantics Interface.
    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, proofs, fstructures) are (...)
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  10. Reinhard Muskens, Higher Order Modal Logic.
    A logic is called higher order if it allows for quantification (and possibly abstraction) over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic (often also called type theory or the Theory of Types) 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 (...)
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  11. Reinhard Muskens, Synonymy, Common Knowledge, and the Social Construction of Meaning.
    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 (...)
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  12. Reinhard Muskens, Separating Syntax and Combinatorics in Categorial Grammar.
    The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...)
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  13. Reinhard Muskens, The Dynamics of Discourse Situations (Extended Abstract).
    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 (...)
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  14. Stefan Wintein & Reinhard Muskens (2012). A Calculus for Belnap's Logic in Which Each Proof Consists of Two Trees. Logique Et Analyse 220:643-656.
     
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  15. Reinhard Muskens (2011). A Squib on Anaphora and Coindexing. Linguistics and Philosophy 34 (1):85-89.
    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 themselves to so that (...)
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  16. Reinhard Muskens (2010). New Directions in Type-Theoretic Grammars. Journal of Logic, Language and Information 19 (2):129-136.
    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 lambda term representing its manifestation, (...)
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  17. Reinhard Muskens (2007). Intensional Models for the Theory of Types. Journal of Symbolic Logic 72 (1):98-118.
    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, it (...)
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  18. Reinhard Muskens (2005). Sense and the Computation of Reference. Linguistics and Philosophy 28 (4):473 - 504.
    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 (...)
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  19. Reinhard Muskens (2004). Order-Independence and Underspecification. In Hans Kamp & Barbara Hall Partee (eds.), Context-Dependence in the Analysis of Linguistic Meaning. Elsevier. 11--239.
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  20. Reinhard Muskens (2003). Language, Lambdas, and Logic. In. In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora. Kluwer. 23--54.
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  21. Reinhard Muskens (2001). Talking About Trees and Truth-Conditions. Journal of Logic, Language and Information 10 (4):417-455.
    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 description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...)
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  22. Reinhard Muskens (2000). Underspecified Semantics. In. In Klaus von Heusinger & Urs Egli (eds.), Reference and Anaphoric Relations. Kluwer. 311--338.
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  23. Reinhard Muskens (1999). On Partial and Paraconsistent Logics. Notre Dame Journal of Formal Logic 40 (3):352-374.
    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 logics once the right (...)
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  24. Reinhard Muskens, Program Semantics and Classical Logic.
    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\/} holds in this new setting, prove soundness (...)
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  25. Reinhard Muskens (1996). Combining Montague Semantics and Discourse Representation. Linguistics and Philosophy 19 (2):143 - 186.
    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.
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  26. Michel Aurnague, Emibl Krahmer & Reinhard Muskens (1995). Cqnte Nts. Journal of Semantics 12.
     
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  27. Emiel Krahmer & Reinhard Muskens (1995). Negation and Disjunction in Discourse Representation Theory. Journal of Semantics 12 (4):357-376.
    Classical Discourse Representation Theory (DRT) predicts that an indefinite noun phrase cannot antecede an anaphoric element if the noun phrase is, but the anaphoric element is not, in the scope of a negation; the theory also predicts that no anaphoric links are possible between the two parts of a disjunction. However, it is well known that these predictions meet with counterexamples. In particular, anaphora is often possible if a double negation intervenes between antecedent and anaphoric element, and also if the (...)
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  28. Reinhard Muskens (1995). Tense and the Logic of Change. In [Book Chapter].
    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.
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  29. Reinhard Anton Muskens (1995). A Bibliography of Publications of Reinhard Anton Muskens. Journal of Semantics 12 (357):357-376.
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  30. Reinhard Muskens, Categorial Grammar and Discourse Representation Theory.
    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.
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  31. Reinhard Muskens (1993). Partial Information. In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics. Pergamon. 6--2952.
    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 (...)
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  32. Reinhard Muskens (1993). Perception Verbs. In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics. Pergamon Press. 6--2999.
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  33. Reinhard Muskens (1993). Propositional Attitudes. In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics. Pergamon Press.
    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.
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  34. Reinhard Muskens (1991). Anaphora and the Logic of Change. In [Book Chapter].
    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.
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  35. Reinhard Muskens (1991). [Book Chapter]. Springer Netherlands.
    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 description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...)
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  36. Reinhard Muskens (1991). Hyperfine-Grained Meanings in Classical Logic. Logique Et Analyse 133:159-176.
    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 involved with (...)
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  37. Reinhard Muskens (1989). A Relational Formulation of the Theory of Types. Linguistics and Philosophy 12 (3):325 - 346.
    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.
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  38. Reinhard Muskens, Coreference.
    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 (...)
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