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A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL*formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for reasoning (...) 

We present Logical Description Grammar (LDG), a model ofgrammar and the syntaxsemantics 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 truthconditionsof 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 truthconditions as a model, it completely specifies thatgrammatical (...) 

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 readings (...) 

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the settheoretic relationships between these classes of trees and between their corresponding firstorder theories. We then obtain some general results about the axiomatization of the firstorder theories of some of these classes of trees in terms of (...) 

A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL$^{*}$formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for reasoning (...) 

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 (...) 

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is nondirectional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators. 

This paper introduces λgrammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λgrammars are multidimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λterms 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. 

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of Marcus et al. 1983 has been integrated in VijayShanker 1992 with a pure unification approach to Lexicalized TreeAdjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic information, that is, we propose to (...) 