Results 11  20
of
422
A MultipleConclusion MetaLogic
 In Proceedings of 9th Annual IEEE Symposium On Logic In Computer Science
, 1994
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic pro ..."
Abstract

Cited by 87 (7 self)
 Add to MetaCart
(Show Context)
The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends the languages λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. As a metalanguage, Forum greatly extends the expressiveness of these other logic programming languages. To illustrate its expressive strength, we specify in Forum a sequent calculus proof system and the operational semantics of a functional programming language that incorporates such nonfunctional features as counters and references. 1
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
Abstract

Cited by 86 (28 self)
 Add to MetaCart
(Show Context)
The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
Elf: A Language for Logic Definition and Verified Metaprogramming
 In Fourth Annual Symposium on Logic in Computer Science
, 1989
"... We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic ..."
Abstract

Cited by 81 (7 self)
 Add to MetaCart
(Show Context)
We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic definition (in the style of LF, the Edinburgh Logical Framework) with logic programming (in the style of Prolog). It achieves this unification by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Hornclauses) an operational interpretation. Novel features of Elf include: (1) the Elf search process automatically constructs terms that can represent objectlogic proofs, and thus a program need not construct them explicitly, (2) the partial correctness of metaprograms with respect to a given logic can be expressed and proved in Elf itself, and (3) Elf exploits Elliott's unification algorithm for a calculus with dependent types. This research was...
Cutelimination for a logic with definitions and induction
 Theoretical Computer Science
, 1997
"... In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The l ..."
Abstract

Cited by 72 (22 self)
 Add to MetaCart
(Show Context)
In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The literature contains many approaches to formally adding these reasoning principles with logic specifications. We choose an approach based on the sequent calculus and design an intuitionistic logic F Oλ ∆IN that includes natural number induction and a notion of definition. We have detailed elsewhere that this logic has a number of applications. In this paper we prove the cutelimination theorem for F Oλ ∆IN, adapting a technique due to Tait and MartinLöf. This cutelimination proof is technically interesting and significantly extends previous results of this kind. 1
Microplanning with Communicative Intentions: The SPUD System
 Computational Intelligence
, 2001
"... The process of microplanning encompasses a range of problems in Natural Language Generation (NLG), such as referring expression generation, lexical choice, and aggregation, problems in which a generator must bridge underlying domainspecific representations and general linguistic representations. In ..."
Abstract

Cited by 71 (16 self)
 Add to MetaCart
(Show Context)
The process of microplanning encompasses a range of problems in Natural Language Generation (NLG), such as referring expression generation, lexical choice, and aggregation, problems in which a generator must bridge underlying domainspecific representations and general linguistic representations. In this paper, we describe a uniform approach to microplanning based on declarative representations of a generator's communicative intent. These representations describe the RE SULTS of NLG: communicative intent associates the concrete linguistic structure planned by the generator with inferences that show how the meaning of that structure communicates needed information about some application domain in the current discourse context. Our approach, implemented in the SPUD (sentence planning using description) microplanner, uses the lexicalized treeadjoining grammar formalism (LTAG) to connect structure to meaning and uses modal logic programming to connect meaning to context. At the same time, communicative intent representations provide a RESOURCE for the PROCESS of NLG. Using representations of communicative intent, a generator can augment the syntax, semantics and pragmatics of an incomplete sentence simultaneously, and can assess its progress on the various problems of microplanning incrementally. The declarative formulation of communicative intent translates into a welldefined methodology for designing grammatical and conceptual resources which the generator can use to achieve desired microplanning behavior in a specified domain. Contents 1 Motivation 3 2
A Uniform ProofTheoretic Investigation Of Linear Logic Programming
, 1994
"... In this paper we consider the problem of identifying logic programming languages for linear logic. Our analysis builds on a notion of goaldirected provability, characterized by the socalled uniform proofs, previously introduced for minimal and intuitionistic logic. A class of uniform proofs in lin ..."
Abstract

Cited by 71 (21 self)
 Add to MetaCart
In this paper we consider the problem of identifying logic programming languages for linear logic. Our analysis builds on a notion of goaldirected provability, characterized by the socalled uniform proofs, previously introduced for minimal and intuitionistic logic. A class of uniform proofs in linear logic is identified by an analysis of the permutability of inferences in the linear sequent calculus. We show that this class of proofs is complete (for logical consequence) for a certain (quite large) fragment of linear logic, which thus forms a logic programming language. We obtain a notion of resolution proof, in which only one left rule, of clausedirected resolution, is required. We also consider a translation, resembling those of Girard, of the hereditary Harrop fragment of intuitionistic logic into our framework. We show that goaldirected provability is preserved under this translation.
Focusing and Polarization in Linear, Intuitionistic, and Classical Logics
, 2009
"... A focused proof system provides a normal form to cutfree proofs in which the application of invertible and noninvertible inference rules is structured. Within linear logic, the focused proof system of Andreoli provides an elegant and comprehensive normal form for cutfree proofs. Within intuitioni ..."
Abstract

Cited by 69 (28 self)
 Add to MetaCart
(Show Context)
A focused proof system provides a normal form to cutfree proofs in which the application of invertible and noninvertible inference rules is structured. Within linear logic, the focused proof system of Andreoli provides an elegant and comprehensive normal form for cutfree proofs. Within intuitionistic and classical logics, there are various different proof systems in the literature that exhibit focusing behavior. These focused proof systems have been applied to both the proof search and the proof normalization approaches to computation. We present a new, focused proof system for intuitionistic logic, called LJF, and show how other intuitionistic proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing. We also use LJF to design a focused proof system LKF for classical logic. Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard’s LC and LU proof systems.
Implementing Tactics and Tacticals in a HigherOrder Logic Programming Language
 Journal of Automated Reasoning
, 1993
"... We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement tactic style theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped terms ..."
Abstract

Cited by 68 (15 self)
 Add to MetaCart
(Show Context)
We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement tactic style theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped terms, replacing firstorder unification with higherorder unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of inference systems can be naturally specified in this language. The higherorder features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many inference systems. Tactics and tacticals, which provide a framework for highlevel control over search for proofs, can be directly and naturally implemented in the extended language. This framework serves as a starting point for implementing theorem provers an...
Efficient resource management for linear logic proof search
 Proceedings of the 5th International Workshop on Extensions of Logic Programming
, 1996
"... The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf). Among these, the problem of efficiently managing the li ..."
Abstract

Cited by 66 (13 self)
 Add to MetaCart
(Show Context)
The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in nontrivial applications. This paper studies this problem in the case of Lolli [HM94], though its results have application to other systems. We first give a prooftheoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the nondeterminism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system. 1
Structural Cut Elimination  I. Intuitionistic and Classical Logic
 Information and Computation
, 2000
"... this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced b ..."
Abstract

Cited by 64 (21 self)
 Add to MetaCart
(Show Context)
this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced by three nested structural inductions. Parameters are treated as variables bound in derivations, thus naturally capturing occurrence conditions. A starting point for the proofs is Kleene's sequent system G 3 [Kle52], which we derive systematically from the point of view that a sequent calculus should be a calculus of proof search for natural deductions. It can easily be related to Gentzen's original and other sequent calculi. We augment G 3 with proof terms that are stable under weakening. These proof terms enable the structural induction and furthermore form the basis of the representation of the proof in LF. The most closely related work on cut elimination is MartinLo# f 's proof of admissibility [ML68]. In MartinLo# f 's system the cut rule incorporates aspects of both weakening and contraction which enables a structural induction argument closely related to ours. However, without the introduction of proof terms, the implicit weakening in the cut rule makes it difficult to implement this proof directly. Herbelin [Her95] restates this proof and proceeds by assigning proof terms only to restricted sequent calculi LJT and LKT which correspond more immediately to