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Equational axioms for probabilistic bisimilarity
 IN PROCEEDINGS OF 9TH AMAST, LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending ..."
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Cited by 21 (1 self)
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the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.
The ground axiom
 J. Symbolic Logic
"... Abstract. A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is firstorder expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many w ..."
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Cited by 14 (2 self)
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wellknown settheoretic assertions including the Generalized Continuum Hypothesis, the assertion v=hod that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set forcing extension of a model
Extensions of finite generalized quadrangles
 In Symposia Mathematica, Vol. XXVIII
, 1983
"... 1.1 Axioms and definitions.................................... 1 1.2 Restrictions on the parameters............................... 2 1.3 Regularity, antiregularity, semiregularity, and property (H)............... 3 ..."
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Cited by 178 (14 self)
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1.1 Axioms and definitions.................................... 1 1.2 Restrictions on the parameters............................... 2 1.3 Regularity, antiregularity, semiregularity, and property (H)............... 3
The AXIOM System
"... . AXIOM* is a computer algebra system superficially like many others, but fundamentally different in its internal construction, and therefore in the possibilities it offers to its users. In these lecture notes, we will ffl outline the highlevel design of the AXIOM kernel and the AXIOM type system, ..."
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Cited by 7 (0 self)
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, ffl explain some of the algebraic facilities implemented in AXIOM, which may be more general than the reader is used to, ffl show how the type system and the information system interact, ffl give some references to the literature on particular aspects of AXIOM, and ffl suggest the way forward. A
On rpsseparation axioms
 International Journal of Modern Engineering Research (Accepted
"... The authors introduced rpsclosed sets and rpsopen sets in topological spaces and established their relationships with some generalized sets in topological spaces. The aim of this paper is to introduce rpsT, rpsT, rpsTb, rpsT spaces and characterize their basic properties. MSC 2010:54D10 ..."
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The authors introduced rpsclosed sets and rpsopen sets in topological spaces and established their relationships with some generalized sets in topological spaces. The aim of this paper is to introduce rpsT, rpsT, rpsTb, rpsT spaces and characterize their basic properties. MSC 2010:54D10
STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY
, 1997
"... This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the ..."
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Cited by 260 (14 self)
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This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors
AXIOM OF CHOICE.
"... The axiom of choice is a statement in the language of set theory (q.v.). It asserts that whenever S is a set such that each member of S is in turn a nonempty set, and such that each pair of members of S have no elements in common, then there exists a set C containing exactly one element from each m ..."
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is not in the set. In general, S could have many choice sets. The axiom of choice merely asserts that it has at least one, without saying how one is to be made. It is this nonconstructive feature that has led to some controversy regarding the acceptability of the axiom. When the set S is finite, then even without
The choice axiom after twenty years
 Journal of Mathematical Psychology
, 1977
"... This survey is divided into three major sections. The first concerns mathematical results about the choice axiom and the choice models that devoIve from it. For example, its relationship to Thurstonian theory is satisfyingly understood; much is known about how choice and ranking probabilities may re ..."
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Cited by 80 (0 self)
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that are at best approximate. And the third section concerns alternative, more general theories which, in spirit, are much like the choice axiom. Perhaps I had best admit at the outset that, as a commentator on this scene, I am qualified no better than many others and rather less well than some who have been
On the Three Axioms of General Design Theory
 Proceedings of the International Workshop of Emergent Synthesis '02
, 2002
"... Yoshikawa’s General Design Theory is an axiomatic theory of design in which design is formulated and discussed in terms of topological spaces defined by entities, entity concepts, and abstract concepts. The theory is developed on declarations called definitions and axioms of which represents the bas ..."
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Cited by 2 (1 self)
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Yoshikawa’s General Design Theory is an axiomatic theory of design in which design is formulated and discussed in terms of topological spaces defined by entities, entity concepts, and abstract concepts. The theory is developed on declarations called definitions and axioms of which represents
EXPECTED UTILITY WITH PURELY SUBJECTIVE NONADDITIVE PROBABILITIES
, 1987
"... Acts are functions from the set of states of the world into the set of consequences. Savage proposed axioms regarding a binary relation on the set of acts which are necessary and sufficient for it to be representable by the functional gu(.)dP for some realvalued (utility) function u on the set of c ..."
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Cited by 217 (2 self)
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of consequences and a (probability) measure P on the set of states of the world. The Ellsberg paradox leads us to reject one of Savage’s main axioms the Sure Thing Principleand develop a more general theory, in which the probability measure need not be additive.
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