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Modular Proof Systems for Partial Functions with Weak Equality
[chapter]

2004
*
Lecture Notes in Computer Science
*

The paper presents a

doi:10.1007/978-3-540-25984-8_10
fatcat:lbcoqguwvrefnnzi2ogsvmazgi
*modular*superposition calculus*for*the combination of first-order theories involving both total and*partial**functions*. ... Finally we identify cases where the*partial*models can always be made total so that*modular*superposition is also complete*with*respect to the standard (total*function*) semantics of the theories. ...*Partial**Functions**with**Weak**Equality*A signature Σ is the disjoint union of a set Σ T of total*function*symbols and a set Σ P of*partial**function*symbols. ...##
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Page 1307 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

of the identity

*function*and codes n+ 1 by an index*for*the constant*function**with*value n. ... One can also expand & to have among its terms the 5s», func- tions (i.e., g(s(a,b),x) = g(a,x,b)*with*suitable subscripts) and the characteristic*function*of*equality*. ...##
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Page 9 of Mathematical Reviews Vol. , Issue 90M
[page]

1990
*
Mathematical Reviews
*

The concept of a

*partial*pair leads to several types of*equality*,*for*instance Kleene*equality*, strong*equality*,*weak**equality*, left to right directional*equality*, and others. ... 90m: 3058 03C Model theory See also 03017, 03019, 03090, 08008, 12014, 18009. 90m:03058 03C05 Craig, William (1-CA) Near-equational and equational*systems*of logic*for**partial**functions*. I J. ...##
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Matroids over partial hyperstructures
[article]

2018
*
arXiv
*
pre-print

We give "cryptomorphic" axiom

arXiv:1709.09707v2
fatcat:r2ufkj563zhyphwzaltbsgrzka
*systems**for*such matroids in terms of circuits, Grassmann-Plücker*functions*, and dual pairs, and establish some basic duality results. ...*For*example, if F is a particularly nice kind of tract called a doubly distributive*partial*hyperfield, we show that the notions of*weak*and strong F-matroids coincide. ... The*proof**for**weak*Grassman-Plücker*functions*is essentially the same, but in the special case that k " 1. ...##
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Modular Control of Discrete-Event Systems With Coalgebra

2008
*
IEEE Transactions on Automatic Control
*

These results are generalized to the case of modules

doi:10.1109/tac.2007.915164
fatcat:zhmfaiwnkjhdnhgg6gricmzwt4
*with**partial*observations: e.g.*modular*computation of supremal normal sublanguages is studied. ...*Modular*supervisory control of discrete-event*systems*(DES), where the overall*system*is composed of subsystems that are combined in synchronous (parallel) product, is considered. ... Financial support of the EU Esprit LTR Project Control and Computation, ISO-2001-33520 and*partial*financial support of the Grant GA AV No. B100190609 is gratefully acknowledged. ...##
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Supremal normal sublanguages of large distributed discrete-event systems

2004
*
IFAC Proceedings Volumes
*

Coalgebraic methods provide new results and insights

doi:10.1016/s1474-6670(17)30725-5
fatcat:fknig47pwjg7rh6n7gjcypiuim
*for**modular*supervisory control of discrete-event*systems*(DES), where the overall*system*is composed of subsystems that are themselves*partially*observed ... The coinduction*proof*principle is used to obtain our main result. ... It is to be expected that*for**modular*DES*with**partial*observations the conditions*for*nonblocking are also the same as*for**modular*DES*with*full observations (Wong and Lee, 2002) , however it must still ...##
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Modular proof systems for partial functions with Evans equality

2006
*
Information and Computation
*

The paper presents a

doi:10.1016/j.ic.2005.10.002
fatcat:nbdf4na2ibbppabvatomqr7aja
*modular*superposition calculus*for*the combination of first-order theories involving both total and*partial**functions*. ... Finally, we identify cases where the*partial*models can always be made total so that*modular*superposition is also complete*with*respect to the standard (total*function*) semantics of the theories. ... See www.avacs.org*for*more information. ...##
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On combinations of local theory extensions
[article]

2008
*
arXiv
*
pre-print

We thus obtain criteria both

arXiv:0810.2653v1
fatcat:3yyf67737namzpsmjru7qs5zfi
*for*recognizing wider classes of local theory extensions, and*for**modular*reasoning in combinations of theories over non-disjoint signatures. ... See www.avacs.org*for*more information. ... This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center "Automatic Verification and Analysis of Complex*Systems*" (SFB/TR 14 AVACS) ...##
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Comparing Curried and Uncurried Rewriting

1996
*
Journal of symbolic computation
*

*for*non-left linear

*systems*. The results extend to

*partial*currying (where some subset of the symbols are curried), and imply some

*modularity*properties

*for*unions of applicative

*systems*. ... We show that

*for*all term rewrite

*systems*(whether orthogonal or not) the following properties are preserved by this transformation: strong normalization,

*weak*normalization,

*weak*Church-Rosser, completeness ... Some of the gures were drawn

*with*Paul Taylor's diagram package. ...

##
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Page 1602 of Mathematical Reviews Vol. 57, Issue 5
[page]

1979
*
Mathematical Reviews
*

if there are congruence compatible

*functions*in A satisfying the*weak*Mal’cev conditions corresponding to e=g. ... The author gives an ingenious*proof*that this is the only non- trivial congruence*equality*e=g*with*the following property:*For*any finite algebra A, e=g holds in the congruence lattice of A if and only ...##
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On the suitability of trace semantics for modular proofs of communicating processes

1985
*
Theoretical Computer Science
*

A trace model

doi:10.1016/0304-3975(85)90130-6
fatcat:qmd5kdh3hncujohhys6rf4uk4u
*for*communicating processes is described and shown to be suitable*for*the construction of a*modular**proof**system*in which*partial*correctness assertions about communicating processes can ... The question of whether a semantic model is suitable*for*the construction of a*modular**proof**system*is studied in detail. ... Discussions*with*P. Eklund and P. Orponen were very helpful. ...##
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Combining algebraic rewriting, extensional lambda calculi, and fixpoints

1996
*
Theoretical Computer Science
*

We show that confluence and strong normalization are

doi:10.1016/s0304-3975(96)00121-1
fatcat:3wj6hg4vobfxzoxumonlv3gvva
*modular*properties*for*the combination of algebraic rewriting*systems**with*typed lambda calculi enriched*with*expansive extensional rules*for*q and ... It is*equally*well known that confluence fails when adding either the usual contraction rule*for*II, or recursion together*with*the usual contraction rule*for*sujective pairing. ... We have also shown how to deal in full generality*with*fixpoint combinators: confluence is preserved under very permissive hypotheses, so that*for*many interesting calculi it is now possible to focus on ...##
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Product Line Selection and Pricing with Modularity in Design

2005
*
Manufacturing & Service Operations Management
*

Finally, we show that the optimal product line length is monotonic in risk attitude and the monotonic

doi:10.1287/msom.1050.0077
fatcat:tldt5cdpbvgijpfftojnx6sv3a
*weak*majorization,*partial*order on product assortment. ... T his paper addresses the strategic impact of*modular*design on the optimal length and price of a differentiated product line. We represent consumer demand*with*a Bayesian logit model. ... Acknowledgments This work was*partially*supported by the National Science Foundation under Grant No. DMI-0114598. ...##
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Complexity of Detectability, Opacity and A-Diagnosability for Modular Discrete Event Systems
[article]

2017
*
arXiv
*
pre-print

Consequently, if the

arXiv:1710.02877v1
fatcat:a6wdyfwntng3bc54hxetfiyqem
*systems*are all fully observable, then deciding*weak*detectability (opacity)*for**modular**systems*is PSPACE-complete. ... In this paper, we study the complexity of deciding*weak*detectability (opacity, A-diagnosability)*for**modular**systems*. ... Deciding*modular*A-diagnosability is EXPSPACE-complete.*Proof*. Checking A-diagnosability*for*a monolithic*system*can be done in PSPACE [1, 4] , and hence EXPSPACE is sufficient*for**modular**systems*. ...##
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Holomorphic projections and Ramanujan's mock theta functions

2014
*
Proceedings of the National Academy of Sciences of the United States of America
*

We use spectral methods of automorphic forms to establish a holomorphic projection operator

doi:10.1073/pnas.1311621111
pmid:24591582
pmcid:PMC3964039
fatcat:yri5t7cglrdmrijltyab2nmukq
*for*tensor products of vector-valued harmonic*weak*Maass forms and vector-valued*modular*forms. ... M ock theta*functions*have a long history but recent work establishes surprising connections*with*different areas of mathematics and physics. ... M.R. was*partially*supported by the Eidgenössische Technische Hochschule Zurich Postdoctoral Fellowship Program and by the Marie Curie Actions*for*People, Co-funding of Regional, National, and International ...
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