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Implicational (semilinear) logics II: additional connectives and characterizations of semilinearity

Archive for Mathematical Logic, 2015
The paper is a continuation of [the authors, Arch. Math. Logic 49, No. 4, 417--446 (2010; Zbl 1196.03013)]. An abstract algebraic logic \(L\) with implication \(\Rightarrow\) is semilinear if the following meta-rule holds: \[ \frac{\Gamma,\phi \Rightarrow \psi \vdash_L \chi \quad \Gamma,\psi \Rightarrow \phi \vdash_L \chi}{\Gamma \vdash_L \chi}.
Petr Cintula, Carles Noguera
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Semilinear Program Feasibility

2009
We study logical techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems (CSPs). For the fundamental algebraic structure $\Gamma=(\mathbb R; L_1,L_2,\dots)$ where $\mathbb R$ are the real numbers and L 1 ,L 2 ,...
Manuel Bodirsky   +2 more
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Semilinearity as a syntactic invariant

1997
Mildly context sensitive grammar formalisms such as multi-component TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a non-semilinear language.
Michaelis, Jens   +2 more
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Semilinear observation systems

Systems & Control Letters, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mahmoud Baroun   +3 more
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Semilinear cell decomposition

Journal of Symbolic Logic, 1994
AbstractWe obtain a p-adic semilinear cell decomposition theorem using methods developed by Denef in [Journal für die Reine und Angewandte Mathematik, vol. 369 (1986), pp. 154–166]. We also prove that any set definable with quantifiers in (0,1, +, —, λq, Pn){n∈ℕ,q∈ℚp} may be defined without quantifiers, where λq is scalar multiplication by q and Pn is ...
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Semilinear operators

Journal of Mathematical Physics, 1988
Semilinear operators on a complex Hilbert space are studied in a part of a program that aims to develop the theories of additive operators on complex and quaternionic Hilbert spaces for application to problems in mathematical physics. The more notable among the new results proved on the eigenvalue problem for semilinear operators are the following: (i)
Sharma, C. S., Almeida, D. F.
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On the Boundedness Property of Semilinear Sets

2013
An additive system to generate a semilinear set is k-bounded if it can generate any element of the set by repeatedly adding vectors according to its rules so that pairwise differences between components in any intermediate vector are bounded by k except for those that have achieved their final target value.
Oscar H. Ibarra, Shinnosuke Seki 0001
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Ultrahomogeneous Semilinear Spaces

Proceedings of the London Mathematical Society, 2002
Recall that a semilinear space \(S\) is a non-empty set of elements called points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Note that semilinear spaces are a common generalization of graphs and of linear spaces.
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Semilinear Motion Planning in REDLOG

Applicable Algebra in Engineering, Communication and Computing, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The complexity of semilinear sets

1980
In this paper we shall characterize the computational complexity of two decision problems: the inequality problem and the uniform word problem for semilinear sets. It will be proved that the first problem is log-complete in the second class (Σp2) of the polynomial-time hierarchy and the second problem is log-complete in NP.
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