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59
Underapproximating predicate transformers
 In Proc. SAS’06, LNCS
, 2006
"... Abstract. We study the underapproximation of the predicate transformers used to give semantics to the modalities in dynamic and temporal logic. Because predicate transformers operate on state sets, we define appropriate powerdomains for sound approximation. We study four such domains — two are based ..."
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Cited by 9 (4 self)
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Abstract. We study the underapproximation of the predicate transformers used to give semantics to the modalities in dynamic and temporal logic. Because predicate transformers operate on state sets, we define appropriate powerdomains for sound approximation. We study four such domains — two are based on “set inclusion ” approximation, and two are based on “quantification ” approximation — and we apply the domains to synthesize the most precise, underapproximating �pre and pre transformers, in the latter case, introducing a focus operation. We also show why the expected abstractions of post and �post are unsound, and we use the powerdomains to guide us to correct, sound underapproximations. 1
Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy
"... Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as s ..."
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Cited by 7 (7 self)
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Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Beginning with the role of number theory in expressing data, we show how we can naturally proceed to hierarchical structures. We show how this both encapsulates traditional paradigms in data analysis, and also opens up new perspectives towards issues that are on the order of the day, including data mining of massive, high dimensional, heterogeneous data sets. Linkages with other fields are also discussed including computational logic and symbolic dynamics.
Free modal algebras: a coalgebraic perspective
"... Abstract. In this paper we discuss a uniform method for constructing free modal and distributive modal algebras. This method draws on works by (Abramsky 2005) and (Ghilardi 1995). We revisit the theory of normal forms for modal logic and derive a normal form representation for positive modal logic. ..."
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Cited by 7 (2 self)
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Abstract. In this paper we discuss a uniform method for constructing free modal and distributive modal algebras. This method draws on works by (Abramsky 2005) and (Ghilardi 1995). We revisit the theory of normal forms for modal logic and derive a normal form representation for positive modal logic. We also show that every finitely generated free modal and distributive modal algebra axiomatised by equations of rank 1 is a reduct of a temporal algebra. 1
Permutation complexity via duality between values and orderings
 Physica D
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Formal Concept Analysis applications to Requirements Engineering and Design
, 2004
"... I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Math ..."
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Cited by 5 (1 self)
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I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Maths & Comp. Sc.), B.Info.Tech.(Hons)
Semantics and logic for security protocols
, 2004
"... This paper presents a sound BANlike logic for reasoning about security protocols with theorem prover support. The logic has formulas for sending and receiving messages (with nonces, public and private encryptions etc.), and has both temporal and modal operators (describing the knowledge of particip ..."
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This paper presents a sound BANlike logic for reasoning about security protocols with theorem prover support. The logic has formulas for sending and receiving messages (with nonces, public and private encryptions etc.), and has both temporal and modal operators (describing the knowledge of participants). The logic’s semantics is based on strand spaces. Several (secrecy) formulas are proven for the NeedhamSchroeder(Lowe) and bilateral key exchange protocols, as illustrations. 1
The arity gap of polynomial functions over bounded distributive lattices
 in: 40th IEEE International Symposium on MultipleValued Logic (ISMVL 2010), IEEE Computer Society, Los Alamitos
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Characterization of Rankings Generated by Linear Discriminant Analysis
, 2002
"... Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model. ..."
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Cited by 4 (4 self)
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Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.
Linear extensions of ranked posets, enumerated by descents. A problem of Stanley from the 1981 Banff Conference on Ordered Sets
, 2005
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S.: Representation of Nelson Algebras by Rough Sets Determined by Quasiorders. Algebra Universalis 66
, 2011
"... Abstract. In this paper, we show that every quasiorder R induces a Nelson algebra RS such that the underlying rough set lattice RS is algebraic. We note that RS is a threevalued Lukasiewicz algebra if and only if R is an equivalence. Our main result says that if A is a Nelson algebra defined on an ..."
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Abstract. In this paper, we show that every quasiorder R induces a Nelson algebra RS such that the underlying rough set lattice RS is algebraic. We note that RS is a threevalued Lukasiewicz algebra if and only if R is an equivalence. Our main result says that if A is a Nelson algebra defined on an algebraic lattice, then there exists a set U and a quasiorder R on U such that A ∼ = RS. 1.