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

Harald Ganzinger, Viorica Sofronie-Stokkermans, Uwe Waldmann
2004 Lecture Notes in Computer Science  
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  
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  
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]

Matthew Baker, Nathan Bowler
2018 arXiv   pre-print
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

Jan Komenda, Jan H. van Schuppen
2008 IEEE Transactions on Automatic Control  
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

Jan Komenda, Jan H. Van Schuppen
2004 IFAC Proceedings Volumes  
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

Harald Ganzinger, Viorica Sofronie-Stokkermans, Uwe Waldmann
2006 Information and Computation  
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 for more information.  ... 
doi:10.1016/j.ic.2005.10.002 fatcat:nbdf4na2ibbppabvatomqr7aja

On combinations of local theory extensions [article]

Viorica Sofronie-Stokkermans
2008 arXiv   pre-print
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 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  
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  
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

R.J.R. Back, H. Mannila
1985 Theoretical Computer Science  
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

Roberto Di Cosmo, Delia Kesner
1996 Theoretical Computer Science  
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

Wallace J. Hopp, Xiaowei Xu
2005 Manufacturing & Service Operations Management  
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]

Tomáš Masopust, Xiang Yin
2017 arXiv   pre-print
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

O. Imamo lu, M. Raum, O. K. Richter
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 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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