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tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 70 (6 self)
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This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove completely automatically are given to illustrate certain aspects of TPS’s behavior and problems of theorem proving in higherorder logic. 7
Situations and Individuals
"... This book deals with the semantics of natural language expressions that are commonly taken to refer to individuals: pronouns, definite descriptions and proper names. It claims, contrary to previous theorizing, that they all have a common syntax and semantics, roughly that which is currently associat ..."
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Cited by 46 (1 self)
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This book deals with the semantics of natural language expressions that are commonly taken to refer to individuals: pronouns, definite descriptions and proper names. It claims, contrary to previous theorizing, that they all have a common syntax and semantics, roughly that which is currently associated by philosophers and linguists with definite descriptions as construed in the tradition of Frege. As well as advancing this proposal, I hope to achieve at least one other aim, that of urging semanticists dealing with pronoun interpretation, in particular donkey anaphora, to consider a wider range of theories at all times than is sometimes done at present. I am thinking particularly of the gulf that seems to have emerged between those who practice some version of dynamic semantics (including DRT) and those who eschew this approach and rely on some version of the Etype analysis for donkey anaphora (if they consider this phenomenon at all). In my opinion there is too little work directly comparing the claims of these two schools (for that is what they amount to) and testing them against the data in the way that any two rival theories might be tested. (Irene Heim’s 1990 article in Linguistics and Philosophy does this, and
A Survey on Temporal Reasoning in Artificial Intelligence
, 1994
"... The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligenc ..."
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Cited by 42 (4 self)
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The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligence systems. Specifically during the last 10 years, it has been attracting the attention of many AI researchers. In this survey, the results of this work are analysed. Firstly, Temporal Reasoning is defined. Then, the most important representational issues which determine a Temporal Reasoning approach are introduced: the logical form on which the approach is based, the ontology (the units taken as primitives, the temporal relations, the algorithms that have been developed,. . . ) and the concepts related with reasoning about action (the representation of change, causality, action,. . . ). For each issue the different choices in the literature are discussed. 1 Introduction The notion of time i...
A Theory of Sentience
, 2000
"... 1.1 Four assays of quality................................................................ 4 1.2 The structure of appearance.................................................... 11 1.3 Intrinsic versus relational........................................................ 13 1.4 Four refutations......... ..."
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Cited by 41 (5 self)
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1.1 Four assays of quality................................................................ 4 1.2 The structure of appearance.................................................... 11 1.3 Intrinsic versus relational........................................................ 13 1.4 Four refutations....................................................................... 17 2. Qualities and their Places................................................................ 25 2.1 The appearance of space......................................................... 25 2.2 Some brainmind mysteries..................................................... 26 2.3 Spatial qualia........................................................................... 33 2.4 Appearances partitioned.......................................................... 35 2.5 Ties that bind........................................................................... 38 2.6 Featureplacing introduced...................................................... 43 3 Places Phenomenal and Real............................................................ 47 3.1 Spacetime regions.................................................................. 47 3.2 Three varieties of visual field.................................................. 50 3.3 Why I am not an array of impressions..................................... 55 3.4 Why I am not an intentional object......................................... 58 3.5 Sensory identification.............................................................. 61 3.6 Some examples of sensory reference....................................... 66
TPS: A TheoremProving System for Classical Type Theory
, 1996
"... . This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 17 (0 self)
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. This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higherorder logic. AMS Subject Classification: 0304, 68T15, 03B35, 03B15, 03B10. Key words: higherorder logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theoremproving system for classical type theory ## (Church's typed #calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...
Conditionals and consequences
 Journal of Applied Logic
, 2007
"... Abstract. We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, nonclassical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With r ..."
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Cited by 13 (11 self)
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Abstract. We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, nonclassical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework. 1 Three mistakes Pure Mathematics is the class of all propositions of the form ‘p implies q’... And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member... [45, p.3]. Thus begins the precursor of Principia Mathematica, Russell’s Principles of Mathematics, and thus begins the sad and confusing twentieth century tale of implication.
On dynamically presenting a topology course
 Annals of Mathematics and Artificial Intelligence
, 2001
"... www.cs.mdx.ac.uk/imp Authors of traditional mathematical texts often have difficulty balancing the amount of contextual information and proof detail. We propose a simple hypermedia framework that can assist in the organisation and presentation of mathematical theorems and definitions. We describe th ..."
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Cited by 10 (5 self)
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www.cs.mdx.ac.uk/imp Authors of traditional mathematical texts often have difficulty balancing the amount of contextual information and proof detail. We propose a simple hypermedia framework that can assist in the organisation and presentation of mathematical theorems and definitions. We describe the application of the framework to convert an existing course in general topology to a webbased set of materials. A pilot study of the materials indicated a high level of user satisfaction. We discuss further lines of investigation, in particular, the presentation of larger bodies of work. 1
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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Cited by 10 (5 self)
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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
A New Paradox in Type Theory
 Logic, Methodology and Philosophy of Science IX : Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science
, 1994
"... this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and ..."
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Cited by 7 (0 self)
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this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and the axiom of description in impredicative Type Theories. 1 Minimal and Polymorphic HigherOrder Logic
Frege versus Cantor and Dedekind: On the Concept of Number
, 1997
"... This paper is in honor of my colleague and friend, Leonard Linsky, on the occasion of his retirement. I presented the earliest version in the Spring of 1992 to a reading group, the other members of which were Leonard Linsky, Steve Awodey, Andre Carus and Mike Price. I presented later versions in the ..."
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Cited by 7 (1 self)
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This paper is in honor of my colleague and friend, Leonard Linsky, on the occasion of his retirement. I presented the earliest version in the Spring of 1992 to a reading group, the other members of which were Leonard Linsky, Steve Awodey, Andre Carus and Mike Price. I presented later versions in the autumn of 1992 to the philosophy colloquium at McGill University and in the autumn of 1993 to the philosophy colloquium at CarnegieMellon University. The discussions following these presentations were valuable to me and I would especially like to acknowledge Emily Carson (for comments on the earliest draft), Michael Hallett, Kenneth Manders, Stephen Menn, G.E. Reyes, Teddy Seidenfeld, and Wilfrid Sieg and the members of the reading group for helpful comments. But, most of all, I would like to thank Howard Stein and Richard Heck, who read the penultimate draft of the paper and made extensive comments and corrections. Naturally, none of these scholars, except possibly Howard Stein, is respon