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Lp, A Logic for Representing and Reasoning with Statistical Knowledge
, 1990
"... This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an importa ..."
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This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...
Probabilistic role models and the guarded fragment
 In Proceedings IPMU2004
, 2004
"... We propose a uniform semantic framework for interpreting probabilistic concept subsumption and probabilistic role quantification through statistical sampling distributions. This general semantic principle serves as the foundation for the development of a probabilistic version of the guarded fragment ..."
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We propose a uniform semantic framework for interpreting probabilistic concept subsumption and probabilistic role quantification through statistical sampling distributions. This general semantic principle serves as the foundation for the development of a probabilistic version of the guarded fragment of firstorder logic. A characterization of equivalence in that logic in terms of bisimulations is given. 1
A General Mathematics of Names
 Information and Computation
, 2007
"... We introduce FMG (FraenkelMostowski Generalised) set theory, a generalisation of FM set theory which allows binding of infinitely many names instead of just finitely many names. We apply this generalisation to show how three presentations of syntax — de Bruijn indices, FM sets, and namecarrying sy ..."
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Cited by 7 (4 self)
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We introduce FMG (FraenkelMostowski Generalised) set theory, a generalisation of FM set theory which allows binding of infinitely many names instead of just finitely many names. We apply this generalisation to show how three presentations of syntax — de Bruijn indices, FM sets, and namecarrying syntax — have a relation generalising to all sets and not only sets of syntax trees. We also give syntaxfree accounts of Barendregt representatives, scope extrusion, and other phenomena associated to αequivalence. Our presentation uses a novel presentation based not on a theory but on a concrete model U.
Extending a Resolution Prover for Inequalities on Elementary Functions
 In Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), LNCS 4790
, 2007
"... Abstract. Experiments show that many inequalities involving exponentials and logarithms can be proved automatically by combining a resolution theorem prover with a decision procedure for the theory of real closed fields (RCF). The method should be applicable to any functions for which polynomial upp ..."
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Cited by 6 (4 self)
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Abstract. Experiments show that many inequalities involving exponentials and logarithms can be proved automatically by combining a resolution theorem prover with a decision procedure for the theory of real closed fields (RCF). The method should be applicable to any functions for which polynomial upper and lower bounds are known. Most bounds only hold for specific argument ranges, but resolution can automatically perform the necessary case analyses. The system consists of a superposition prover (Metis) combined with John Harrison’s RCF solver and a small amount of code to simplify literals with respect to the RCF theory. 1
The Calculator Project  Formal Reasoning about Programs
, 1995
"... This paper describes The Calculator Project, which was a threeyear joint research project between the Centre for Information Technology in Education at The Open University, U.K. (Pat Fung, Tim O'Shea) and the Department of Computer Science, QMW, University of London, U.K. (Richard Bornat, Doug Gold ..."
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This paper describes The Calculator Project, which was a threeyear joint research project between the Centre for Information Technology in Education at The Open University, U.K. (Pat Fung, Tim O'Shea) and the Department of Computer Science, QMW, University of London, U.K. (Richard Bornat, Doug Goldson, Mike Hopkins, Steve Reeves). The project was funded by the U.K. Joint Council Initiative in Cognitive Science and HumanComputer Interaction. The central aim of the project was to test the hypothesis that providing socalled calculators would improve students' performance in those parts of the undergraduate firstyear that relied on formal reasoning skills. 1: Introduction Computer Science undergraduates find "formal methods", i.e. the use of mathematical notations and methods for supporting the development of computer software and systems, difficult and in particular they find the part of formal methods that demands reasoning about their programs the most difficult. The work reported...
Formal specification of user interface design guidelines
, 2005
"... Formal specification allows us to design and model the behaviour of computer systems and test their correctness prior to implementation. For any sort of computer system, the problems of being sure you have asked for the right thing (validating the specification against the user’s requirements) and t ..."
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Formal specification allows us to design and model the behaviour of computer systems and test their correctness prior to implementation. For any sort of computer system, the problems of being sure you have asked for the right thing (validating the specification against the user’s requirements) and then being sure you are implementing the right thing (verifying the implementation relative to the specification) are important and hard problems. If the system also has a user interface, which is true in the majority of cases, there are the analogous additional problems of making sure that the interface allows any interaction that is required, and works in a usable way. Graphical user interface design guidelines are used in both the design and evaluation of user interfaces to try and ensure that the systems we build are usable. This project aims to use formal methods to specify systems and their graphical user interfaces and model guidelines for interface design. These will then be used together as the basis for proving the usability properties of a specified system given by the
ObjectOriented Database Evolution
 In Proc. of ICDT'97
"... . An evolution language is composed of an instance update language, a schema update language, and a mechanism to combine them. We present a formal evolution language for objectoriented database management systems. This language allows to write programs to update simultaneously both the schema a ..."
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. An evolution language is composed of an instance update language, a schema update language, and a mechanism to combine them. We present a formal evolution language for objectoriented database management systems. This language allows to write programs to update simultaneously both the schema and the instance. Static checking of these programs insures that the resulting database is consistent. We propose an autonomous instance update language, based on an adequate specific query language and a pure instance update language. The main features of the query language are a formal type inference system including disjunctive types, and the decidability of the satisfiability problem, despite a negation operator. The pure instance update language allows objects migration, and objects and references creation and deletion; its semantics is declarative, and an algorithm to compute it is presented. We propose an evolution mechanism for combining this instance update language with a...
Theory of Finite Trees Revisited: Application of ModelTheoretic Algebra
, 1994
"... . The theory of finite trees in finite signature \Sigma is axiomatized by the simple set of axioms E : 1. 8x x 6= t(x) for every nonvariable term t(x) containing x, 2. 8x 8y ( f(x) = f(y) , x = y ) for every f 2 \Sigma , 3. 8x 8y (f(x) 6= g(y)) for different f , g 2 \Sigma , plus the usual eq ..."
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. The theory of finite trees in finite signature \Sigma is axiomatized by the simple set of axioms E : 1. 8x x 6= t(x) for every nonvariable term t(x) containing x, 2. 8x 8y ( f(x) = f(y) , x = y ) for every f 2 \Sigma , 3. 8x 8y (f(x) 6= g(y)) for different f , g 2 \Sigma , plus the usual equality axioms, plus the following Domain Closure Axiom: 8x f2\Sigma 9z ( x = f(z) ) (DCA) postulating that every element of a model is in the range of some (perhaps 0ary) function, i.e., there are no isolated elements. The theory E [ (DCA) has numerous applications in Automated deduction, Constraint solving, Unification theory, Logic programming, Database theory. It was proved complete by Maher [Mah88] using the straightforward quantifier elimination, and also by Lescanne and Comon [CL89] by a direct transformational method. Earlier Kunen [Kun87] proved that E (without (DCA)) is complete in the case of infinite signatures with constants (this case is much more simple), again by...