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Modular Proof Systems for Partial Functions with Weak Equality
[chapter]
2004
Lecture Notes in Computer Science
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The paper presents a 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. ...
doi:10.1007/978-3-540-25984-8_10
fatcat:lbcoqguwvrefnnzi2ogsvmazgi
Page 1307 of Mathematical Reviews Vol. , Issue 95c
[page]
1995
Mathematical Reviews
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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. ...
Page 9 of Mathematical Reviews Vol. , Issue 90M
[page]
1990
Mathematical Reviews
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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. ...
Matroids over partial hyperstructures
[article]
2018
arXiv
pre-print
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We give "cryptomorphic" axiom 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. ...
arXiv:1709.09707v2
fatcat:r2ufkj563zhyphwzaltbsgrzka
Modular Control of Discrete-Event Systems With Coalgebra
2008
IEEE Transactions on Automatic Control
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These results are generalized to the case of modules 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. ...
doi:10.1109/tac.2007.915164
fatcat:zhmfaiwnkjhdnhgg6gricmzwt4
Supremal normal sublanguages of large distributed discrete-event systems
2004
IFAC Proceedings Volumes
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Coalgebraic methods provide new results and insights 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 ...
doi:10.1016/s1474-6670(17)30725-5
fatcat:fknig47pwjg7rh6n7gjcypiuim
Modular proof systems for partial functions with Evans equality
2006
Information and Computation
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The paper presents a 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. ...
doi:10.1016/j.ic.2005.10.002
fatcat:nbdf4na2ibbppabvatomqr7aja
On combinations of local theory extensions
[article]
2008
arXiv
pre-print
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We thus obtain criteria both 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) ...
arXiv:0810.2653v1
fatcat:3yyf67737namzpsmjru7qs5zfi
Comparing Curried and Uncurried Rewriting
1996
Journal of symbolic computation
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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. ...
doi:10.1006/jsco.1996.0002
fatcat:uniliauis5f3fole6o26elgnrm
Page 1602 of Mathematical Reviews Vol. 57, Issue 5
[page]
1979
Mathematical Reviews
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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 ...
On the suitability of trace semantics for modular proofs of communicating processes
1985
Theoretical Computer Science
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A trace model 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. ...
doi:10.1016/0304-3975(85)90130-6
fatcat:qmd5kdh3hncujohhys6rf4uk4u
Combining algebraic rewriting, extensional lambda calculi, and fixpoints
1996
Theoretical Computer Science
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We show that confluence and strong normalization are 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 ...
doi:10.1016/s0304-3975(96)00121-1
fatcat:3wj6hg4vobfxzoxumonlv3gvva
Product Line Selection and Pricing with Modularity in Design
2005
Manufacturing & Service Operations Management
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Finally, we show that the optimal product line length is monotonic in risk attitude and the monotonic 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. ...
doi:10.1287/msom.1050.0077
fatcat:tldt5cdpbvgijpfftojnx6sv3a
Complexity of Detectability, Opacity and A-Diagnosability for Modular Discrete Event Systems
[article]
2017
arXiv
pre-print
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Consequently, if the 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. ...
arXiv:1710.02877v1
fatcat:a6wdyfwntng3bc54hxetfiyqem
Holomorphic projections and Ramanujan's mock theta functions
2014
Proceedings of the National Academy of Sciences of the United States of America
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We use spectral methods of automorphic forms to establish a holomorphic projection operator 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 ...
doi:10.1073/pnas.1311621111
pmid:24591582
pmcid:PMC3964039
fatcat:yri5t7cglrdmrijltyab2nmukq
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