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This work is licensed under the Creative Commons Attribution License. A Formalization of the Theorem of Existence of First-Order Most General Unifiers∗
"... This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness of the ..."
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This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Loopy belief propagation for approximate inference: An empirical study. In:
- Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
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Cited by 676 (15 self)
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Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon
Unifying class-based representation formalisms
- J. of Artificial Intelligence Research
, 1999
"... The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their c ..."
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Cited by 101 (33 self)
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their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description
Most General First Order Theorems are not Recursively Enumerable
, 1994
"... : An #-substitution is a uniform replacement of n-ary predicates Q n by n-ary 'complex' predicates, that is, by formulas containing all the name form variables of Q n . (In propositional logic, #-substitutions coincide standard substitutions for propositional variables). Formula A is ..."
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(r.e.) logic L extending intuitionistic propositional or first order logic, Gen # (L) is r.e. only if L is decidable. The theorem still holds if L includes modal operators. One of its consequences is that most general first order theorems are not axiomatizable. 1. Introduction 1.1 Preliminaries
THE TIME DIMENSION AND A UNIFIED MATHEMATICAL FRAMEWORK FOR FIRST-ORDER PARABOLIC SYSTEMS
"... For the analysis of problems encompassing linear �rst-order parabolic systems involving the time dimension, the present exposition describes the evolution of and synthesis leading to a general uni�ed mathematical framework and design of computational algorithms. In our previous efforts, various issu ..."
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Cited by 2 (1 self)
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design of computational algorithms is outlined in this article. A generalized stability and accuracy limitation theorem is also highlighted for linear transient algorithms encompassing �rst-order parabolic systems. Characterization as related to computational algorithms pertains to that which not only
Multilanguage Hierarchical Logics (or: How We Can Do Without Modal Logics)
, 1994
"... MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to ..."
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Cited by 212 (52 self)
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to modal logics. The motivations of our proposal are technical, epistemological and implementational. From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first order
Reflecting proofs in first-order logic with equality
- In Proceedings of EUROSPEECH’97
, 2005
"... Abstract. Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equality. Thanks to the reflection ability of Coq, this interpreter is both implemented and formally proved sound — ..."
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Cited by 10 (3 self)
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Abstract. Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equality. Thanks to the reflection ability of Coq, this interpreter is both implemented and formally proved sound
Probabilistic Theorem Proving
"... Many representation schemes combining firstorder logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logic ..."
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Cited by 70 (23 self)
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logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving, their generalization, as the problem of computing
Convergence in formal topology: a unifying notion
, 2013
"... Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We introduce a general notion of convergence of which any previous ..."
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Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We introduce a general notion of convergence of which any previous
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929
