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The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
MultiStage Programming: Its Theory and Applications
, 1999
"... MetaML is a statically typed functional programming language with special support for program generation. In addition to providing the standard features of contemporary programming languages such as Standard ML, MetaML provides three staging annotations. These staging annotations allow the construct ..."
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MetaML is a statically typed functional programming language with special support for program generation. In addition to providing the standard features of contemporary programming languages such as Standard ML, MetaML provides three staging annotations. These staging annotations allow the construction, combination, and execution of objectprograms. Our thesis is that MetaML's three staging annotations provide a useful, theoretically sound basis for building program generators. This dissertation reports on our study of MetaML's staging constructs, their use, their implementation, and their formal semantics. Our results include an extended example of where MetaML allows us to produce efficient programs, an explanation of why implementing these constructs in traditional ways can be challenging, two formulations of MetaML's semantics, a type system for MetaML, and a proposal for extending ...
Types in logic and mathematics before 1940
 Bulletin of Symbolic Logic
, 2002
"... Abstract. In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead’s Principia Mathematica ([71], 1910–1912) and Church’s simply typed λcalculus of 1940. We first argue that the concept of types has always been present in mathematics, thou ..."
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Abstract. In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead’s Principia Mathematica ([71], 1910–1912) and Church’s simply typed λcalculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege’s Grundgesetze der Arithmetik for which Russell applied his famous paradox 1 and this led him to introduce the first theory of types, the Ramified Type Theory (rtt). We present rtt formally using the modern notation for type theory and we discuss how Ramsey, Hilbert and Ackermann removed the orders from rtt leading to the simple theory of types stt. We present stt and Church’s own simply typed λcalculus (λ→C 2) and we finish by comparing rtt, stt and λ→C. §1. Introduction. Nowadays, type theory has many applications and is used in many different disciplines. Even within logic and mathematics, there are many different type systems. They serve several purposes, and are formulated in various ways. But, before 1903 when Russell first introduced
Virtual Transfer Factors
"... Abstract. The LanglandsShelstad transfer factor is a function defined on some reductive groups over a padic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q c sign, where sign ∈ {−1, 0, 1}, q is the cardinality ..."
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Abstract. The LanglandsShelstad transfer factor is a function defined on some reductive groups over a padic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q c sign, where sign ∈ {−1, 0, 1}, q is the cardinality of the residue field, and c is a rational number. The sign function partitions the Lie algebra into three subsets. This article shows that this partition into three subsets is independent of the padic field in the following sense. We define three universal objects (virtual sets in the sense of Quine) such that for any padic field F of sufficiently large residue characteristic, the Fpoints of these three virtual sets form the partition. The theory of arithmetic motivic integration associates a virtual Chow motive with each of the three virtual sets. The construction in this article achieves the first step in a long program to determine the (still conjectural) virtual Chow motives that control the behavior of orbital
An automated prover for ZermeloFraenkel set theory in Theorema
 In LMCS02
"... This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the wellknown Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for sta ..."
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This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the wellknown Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.
Complexity and “Closure to Efficient Cause”
"... This paper has two main purposes. First, it will provide an introductory discussion of hyperset theory, and show that it is useful for modeling complex systems. Second, it will use hyperset theory to analyze Robert Rosen’s metabolismrepair systems and his claim that living things are closed to effic ..."
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This paper has two main purposes. First, it will provide an introductory discussion of hyperset theory, and show that it is useful for modeling complex systems. Second, it will use hyperset theory to analyze Robert Rosen’s metabolismrepair systems and his claim that living things are closed to efficient cause. It will also briefly compare closure to efficient cause to two other understandings of autonomy, operational closure and catalytic closure.
Set Theory and Nominalisation, Part I
 Journal of Logic and Computation
, 1996
"... This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, ..."
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Cited by 2 (2 self)
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This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, we shall set the ground for the second part which demonstrates that Frege structures are a suitable framework for dealing with nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 The Problems We shall examine the problem of the semantics of nominalised terms from two angles: the formal theory and the existence of models. 1.1 The problem of the formal theory Any theory of nominalisation should be accompanied by some ontological views on concepts  for predicates and open wellformed formulae act semantically as concepts. This is vague, however, if only because where I use the word concept, someone else might use class, predicate, set, property or even...
Set Theory and Nominalisation, Part II
 Journal of Logic and Computation
, 1992
"... In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations ..."
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In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations and can be used as models for nominalisation. Hence we develop a type theory based on Frege structures and use it as a theory of nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 Frege structures, a formal introduction Having in part I informally introduced Frege structures, I shall here fill in all the technical details and show that Frege structures exist. Consider F 0 , F 1 ; : : : ; a family F of collections where F 0 is a collection of objects, and (8n ? 0)[F n is a collection of nary functions from F n 0 to F 0 ]. Definition 1.1 (An explicitly closed family) A family F as above is explicitly closed iff: For every expression e[x 1 ; : : : ; x n...
Aspects of Until
, 1999
"... A formal analysis of until within the framework of Dynamic Event Semantics is presented. It derives the frame points of untilclauses from their aspectual class. Keywords: Aspect, Tense, Events, Temporal Logic, Dynamic Semantics 1 Introduction 1.1 Some Data Any analysis of until in English must ..."
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A formal analysis of until within the framework of Dynamic Event Semantics is presented. It derives the frame points of untilclauses from their aspectual class. Keywords: Aspect, Tense, Events, Temporal Logic, Dynamic Semantics 1 Introduction 1.1 Some Data Any analysis of until in English must explain the following two phenomena. First, there is an aspectual restriction on the sentence in the main clause. Only sentences are admitted that are aspectually either of type activity or state, (1a). Sentences of type accomplishment or achievement are excluded, witness (1b). (1) a. John ran=was ill until Mary arrived. b. *John ate an apple=reached the station until Mary arrived. If the accomplishment expression in the main clause is negated, (2a), or progressivized, (2b), the sentence becomes acceptable (similarly for an achievement expression). This change in acceptability is expected because both negation and the progressive trigger an aspectual shift. Expressions of type accomplish...
Understanding Ontologies in Scholarly Disciplines
"... Description logics are valuable for modeling the conceptual structures of scientific and engineering research because the underlying ontologies generally have a taxonomic core. Such structures have natural representations through semantic networks that mirror the underlying description logic grapht ..."
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Description logics are valuable for modeling the conceptual structures of scientific and engineering research because the underlying ontologies generally have a taxonomic core. Such structures have natural representations through semantic networks that mirror the underlying description logic graphtheoretic structures and are more comprehensible than logical notations to those developing and studying the models. This article reports experience in the development of visual language tools for description logics with the objective of making research issues, past and present, more understandable.