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Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 19 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
A New Approach to Predicative Set Theory
"... We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an a ..."
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Cited by 2 (1 self)
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We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. This idea is implemented using syntactic safety relations between formulas and sets of variables. These safety relations generalize both the notion of domainindependence from database theory, and Godel notion of absoluteness from set theory. The language of PZF is typefree, and it reflects real mathematical practice in making an extensive use of statically defined abstract set terms. Another important feature of PZF is that its underlying logic is ancestral logic (i.e. the extension of FOL with a transitive closure operation). 1
Three Conceptual Problems That Bug Me
, 1996
"... Introduction I will talk here about three problems that have bothered me for a number of years, during which time I have experimented with a variety of solutions and encouraged others to work on them. I have raised each of them separately both in full and in passing in various contexts, but thought ..."
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Introduction I will talk here about three problems that have bothered me for a number of years, during which time I have experimented with a variety of solutions and encouraged others to work on them. I have raised each of them separately both in full and in passing in various contexts, but thought it would be worthwhile on this occasion to bring them to your attention side by side. In this talk I will explain the problems, together with some things that have been tried in the past and some new ideas for their solution. Types of conceptual problems. A conceptual problem is not one which is formulated in precise technical terms and which calls for a definite answer. For this reason, there are no clearcut criteria for their solution, but one can bring some criteria to bear. These will vary from case to case. There are three general types of conceptual problems in mathematics of which the ones that I will discuss today are examples. These are: 1 ffi<F