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A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 807 (45 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
PVS: A Prototype Verification System
 CADE
, 1992
"... PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. ..."
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Cited by 654 (16 self)
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PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. It has been used to construct proofs of nontrivial difficulty with relatively modest amounts of human effort. Here, we describe some of the motivation behind PVS and provide some details of the system. Automated reasoning systems typically fall in one of two classes: those that provide powerful automation for an impoverished logic, and others that feature expressive logics but only limited automation. PVS attempts to tread the middle ground between these two classes by providing mechanical assistance to support clear and abstract specifications, and readable yet sound proofs for difficult theorems. Our goal is to provide mechanicallychecked specificati
Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 880 (64 self)
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We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, Flogic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. Flogic has a modeltheoretic semantics and a sound and complete resolutionbased proof theory. A small number of fundamental concepts that come from objectoriented programming have direct representation in Flogic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive objectoriented language based on a subset of Flogic.
The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (49 self)
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Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment. Higherorder logic has several practical advantages over other metalogics. Many proof techniques are known, such as Huet's higherorder unification procedure. Key words: higherorder logic, higherorder unification, Isabelle, LCF, logical frameworks, metareasoning, natural deduction Contents 1 History and overview 2 2 The metalogic M 4 2.1 Syntax of the metalogic ......................... 4 2.2 ...
Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
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Cited by 425 (124 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that firstorder and higherorder Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that firstorder and higherorder versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to firstorder Horn clauses is briefly discussed.
On Language and Connectionism: Analysis of a Parallel Distributed Processing Model of Language Acquisition
 COGNITION
, 1988
"... Does knowledge of language consist of mentallyrepresented rules? Rumelhart and McClelland have described a connectionist (parallel distributed processing) model of the acquisition of the past tense in English which successfully maps many stems onto their past tense forms, both regular (walk/walked) ..."
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Cited by 404 (12 self)
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Does knowledge of language consist of mentallyrepresented rules? Rumelhart and McClelland have described a connectionist (parallel distributed processing) model of the acquisition of the past tense in English which successfully maps many stems onto their past tense forms, both regular (walk/walked) and irregular (go/went), and which mimics some of the errors and sequences of development of children. Yet the model contains no explicit rules, only a set of neuronstyle units which stand for trigrams of phonetic features of the stem, a set of units which stand for trigrams of phonetic features of the past form, and an array of connections between the two sets of units whose strengths are modified during learning. Rumelhart and McClelland conclude that linguistic rules may be merely convenient approximate fictions and that the real causal processes in language use and acquisition must be characterized as the transfer of activation levels among units and the modification of the weights of their connections. We analyze both the linguistic and the developmental assumptions of the model in detail and discover that (1) it cannot represent certain words, (2) it cannot learn many rules, (3) it can learn rules found in no human language, (4) it cannot explain morphological and phonological regularities, (5) it cannot explain the differences between irregular and regular forms, (6) it fails at its assigned task of mastering the past tense of English, (7) it gives an incorrect explanation for two developmental phenomena: stages of overregularization of irregular forms such as bringed, and the appearance of doublymarked forms such as ated, and (8) it gives accounts of two others (infrequent overregularization of verbs ending in t/d, and the order of acquisition of different irregula...
Implementing Mathematics with The Nuprl Proof Development System
, 1986
"... Problem solving is a significant part of science and mathematics and is the most intellectually significant part of programming. Solving a problem involves understanding the problem, analyzing it, exploring possible solutions, writing notes about intermediate results, reading about relevant methods, ..."
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Cited by 190 (18 self)
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, checking results, and eventually assembling a solution. Nuprl is a computer system which provides assistance with this activity. It supports the interactive creation of proofs, formulas, and terms in a formal theory of mathematics
IMPLEMENTING REFLECTION IN NUPRL
, 2006
"... Reflection is the ability of some entity to describe itself. In a logical context, it is the ability of a logic to reason about itself. Reflection is, therefore, placed at the core of metamathematics, making it an important part of formal reasoning; where it revolves mainly around syntax and semant ..."
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and semantics — the main challenge is in making the syntax of the logic become part of its semantic domain. Given its importance, it is surprising that logical computer systems tend to avoid the subject, or provide poor tools for reflective work. This is in sharp contrast to the area of programming languages
System Description: Twelf  A MetaLogical Framework for Deductive Systems
 Proceedings of the 16th International Conference on Automated Deduction (CADE16
, 1999
"... . Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming interp ..."
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Cited by 363 (56 self)
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. Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming
Results 1  10
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