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Page 7662 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
Anna Labella (Rome) 2001k:03026 03B40 68N18 Geuvers, Herman (NL-EIND-C; Eindhoven); Barendsen, Erik (NL-NIJM-CSI; Nijmegen) Some logical and syntactical observations concerning the first-order dependent  ...  Then we discuss two issues in some more detail. The first is the completeness of the formulas-as-types embedding of min- imal first-order predicate logic into AP.  ... 

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

Christian Retoré
2012 Recherches Linguistiques de Vincennes  
To do so, we depart from the Fregean view with a single untyped universe and we adopt a type theory with some hints from Hilbert ε-calculus and from medieval philosophy.  ...  Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics by Asher, Luo and us.  ...  In Montague semantics it is usually higher order predicate logic-although some use first order logic via a reification of predicates.  ... 
doi:10.4000/rlv.2082 fatcat:gaho43wxejbobfosrcf7dlh7l4

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most [article]

Christian Retoré
2012 arXiv   pre-print
Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996).  ...  Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011).  ...  In Montague semantics it is usually higher order predicate logic -although some use first order logic via a reification of predicates.  ... 
arXiv:1203.1743v1 fatcat:fgeongvdgzbepc2vb6jcb656kq

Processing English with a Generalized Phrase Structure Grammar

Jean Mark Gawron, Jonathan King, John Lamping, Egon Loebner, E. Anne Paulson, Geoffrey K. Pullum, Ivan A. Sag, Thomas Wasow
1982 Proceedings of the 20th annual meeting on Association for Computational Linguistics -  
This paper describes a natural language processing system implemented at Hewlett-Packard's Computer Research Center.  ...  We regard it as an important fact about the GPSG system that links computational linguistics to first-order logical representation just as the work referred to above has linked first-order logic to relational  ...  sortal information to convert "normal-form" first-order logical expressions into the query language for HIRE, a relational database hosted in the SPHERE system.  ... 
doi:10.3115/981251.981269 dblp:conf/acl/GawronKLLPPSW82 fatcat:es6w4f4eirddli5rny747srkvy

Categorial Minimalist Grammar [article]

Maxime Amblard, Alain Lecomte (INRIA Bordeaux - Sud-Ouest, SFLTAMP), Christian Retoré
2010 arXiv   pre-print
We first recall some basic notions on minimalist grammars and on categorial grammars.  ...  Thereafter we briefly present \lambda\mu-DRT (Discourse Representation Theory) an extension of \lambda-DRT (compositional DRT) in the framework of \lambda\mu calculus: it avoids type raising and derives  ...  for entities. v the type for reifying events and predicates in order to remain in first order logic.  ... 
arXiv:1012.2661v1 fatcat:bdw3dczvobezhftsxreq3cw26e

Semantic and Syntactic Approaches to Simulation Relations [chapter]

Jo Hannay, Shin-ya Katsumata, Donald Sannella
2003 Lecture Notes in Computer Science  
Meanwhile, second-order prelogical relations directly generalise pre-logical relations to polymorphic lambda calculus (System F).  ...  In the simply-typed lambda calculus, logical relations are the standard choice for simulation relations, but they suffer from certain shortcomings; these are resolved by use of the weaker notion of pre-logical  ...  One reasonable choice for syntactic formalism is the polymorphic lambda calculus, together with a second-order logic, with the lambda calculus being the object programming language.  ... 
doi:10.1007/978-3-540-45138-9_4 fatcat:6ksjb7xqr5byvi4n277qcqsvhy

Reasoning about effects: from lists to cyber-physical agents

Ian A. Mason, Carolyn L. Talcott
2019 Logical Methods in Computer Science  
The next challenge was to consider higher-order programming, adding functions as first class objects to mutable data.  ...  The advent of cyber-physical agents introduces the need to consider uncertainty, faults, physical as well as logical effects.  ...  In computation systems effects are observed by and affect the remaining computation (continuation), the concurrent computations, and observers outside the system.  ... 
doi:10.23638/lmcs-15(2:8)2019 fatcat:wmxqvfisprdltfljbp7zdabzlq

Semantic Bootstrapping of Type-Logical Grammar

Sean A. Fulop
2005 Journal of Logic, Language and Information  
A procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus.  ...  This effort extends the earlier induction of such lexicons for classical categorial grammar (Buszkowski and Penn, 1990) to at first the non-associative Lambek calculus, and then to a large class of type  ...  To handle the equivalence between lambda terms and trees of syntactic types, some preliminaries are needed. DEFINITION 4.2. A tree (i.e.  ... 
doi:10.1007/s10849-005-4509-8 fatcat:c2pobujgjbci5jawmx6e65gt64

Semantic bootstrapping of type-logical grammar

Sean A. Fulop
2004 Journal of Logic, Language and Information  
A procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus.  ...  This effort extends the earlier induction of such lexicons for classical categorial grammar (Buszkowski and Penn, 1990) to at first the non-associative Lambek calculus, and then to a large class of type  ...  To handle the equivalence between lambda terms and trees of syntactic types, some preliminaries are needed. DEFINITION 4.2. A tree (i.e.  ... 
doi:10.1007/s10849-004-4509-0 fatcat:rw4jroblnbd2foqk72wyfd6bqu

Reasoning about effects: from lists to cyber-physical agents [article]

Ian A. Mason, Carolyn L. Talcott
2019 arXiv   pre-print
The next challenge was to consider higher-order programming, adding functions as first class objects to mutable data.  ...  The advent of cyber-physical agents introduces the need to consider uncertainty, faults, physical as well as logical effects.  ...  In computation systems effects are observed by and affect the remaining computation (continuation), the concurrent computations, and observers outside the system.  ... 
arXiv:1801.08450v4 fatcat:y5tcpedn4nfzvage3xq2x7okki

On the use of advanced logic programming languages in computational linguistics

Solange Coupet-Grimal, Olivier Ridoux
1995 The Journal of Logic Programming  
Every A-expression corresponding to some syntactic construct will have the type associated with that construct.  ...  The syntax of definite clauses (D-formulas), goals (G-formulas), and atomic formulas (A-formulas) is as follows: for Prolog as far as the first-order Horn formula fragment of AProlog is concerned.  ...  The authors would like to thank the anonymous reviewers whose comments helped to improve the paper. Thanks must also go to David Trotman and Luke Hornof for their careful reading of the paper.  ... 
doi:10.1016/0743-1066(95)00040-q fatcat:ph7ll7eoinekvll3i6o5ktyqsa

A type theoretical framework for natural language semantics: the Montagovian generative lexicon [article]

Christian Retoré
2014 arXiv   pre-print
Word meaning is depicted by lambda terms of second order lambda calculus (Girard's system F) with base types including a type for propositions and many types for sorts of a many sorted logic.  ...  of a predicate, and the possible adaptation of a word meaning to some contexts.  ...  We use many-sorted higher order predicate calculus. As usual, the higher order can be reified in first order logic, so it can be first order logic, but in any case the logic has to be many sorted.  ... 
arXiv:1301.4938v3 fatcat:jrecwr2nqzgl7ir4grui5kfcqy

The Non-associative Lambek Calculus [chapter]

Richard Moot, Christian Retoré
2012 Lecture Notes in Computer Science  
A type p → q is a function from p to q, while a type p × q is the Cartesian products of p and q. We define the mapping from syntactic categories to types. Definition 28.  ...  Our first remark concerns the weak generative capacity of Lambek syntactic calculus and NL. Both logics generate the same class of languages, namely the context-free languages.  ...  For each case we distinguish various subcases, depending on the rule from which the main premise f : x → y of the main premise of the cut is derived. (7.6) Case: 1.  ... 
doi:10.1007/978-3-642-31555-8_4 fatcat:z6zssyjuprhjxow4rhwwewq6ga

Extending Lambek grammars

Alain Lecomte, Christian Retoré
2001 Proceedings of the 39th Annual Meeting on Association for Computational Linguistics - ACL '01  
data (based on a typing-algorithm and type-unification).  ...  Here we emphasize the connection to Montague semantics which can be viewed as a formal computation of the logical form.  ...  Observe that although entropy which suppresses some order has been used, the labels consist in ordered sequences of phonological and logical forms.  ... 
doi:10.3115/1073012.1073059 dblp:conf/acl/LecomteR01 fatcat:4fohdopunre37kmbxnx3nc7obm

Logical Grammar [chapter]

Glyn Morrill
2012 Philosophy of Linguistics  
ACKNOWLEDGEMENTS This work was partially funded by the DGICYT project TIN2008-06582-C03-01 (SESAAME-BAR). Thanks to Hiroyuki Uchida for comments. All errors are my own.  ...  In section 1 of this article we recall some relevant logical tools: predicate logic, sequent calculus, natural deduction, typed lambda calculus and the Lambek calculus.  ...  The set T of first-order terms and the set F of first-order formulas are defined recursively as follows: T ::= C | V | F i (T 1 , . . . , T i ), i > 0 F ::= P i T 1 . . .  ... 
doi:10.1016/b978-0-444-51747-0.50003-2 fatcat:ywfi5re5brem7f4mvyaiyrq7t4
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