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Basic Constructive Connectives, Determinism and Matrix-Based Semantics [chapter]

Agata Ciabattoni, Ori Lahav, Anna Zamansky
2011 Lecture Notes in Computer Science  
An alternative matrixbased formulation of such semantics is introduced, which provides an algorithm for checking these properties, and also new insights into basic constructive connectives.  ...  Non-)deterministic Kripke-style semantics is used to characterize two syntactic properties of single-conclusion canonical sequent calculi: invertibility of rules and axiom-expansion.  ...  Two F-semiframes W 1 and W 2 agree on some ψ ∈ F, if either both are models of ⇒ ψ, or both are not models of ⇒ ψ.  ... 
doi:10.1007/978-3-642-22119-4_11 fatcat:qlxlmpo4wfds7hbjvmjs57zyai

Page 3446 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
In this paper, new constructions for these designs are provided with some series of designs with k = 3. Cyclic semiframes are discussed.  ...  {For the entire collection see MR 98e:05001.} 98f:05036 05B30 Kageyama, Sanpei (J-HROSE-M2; Higashi-Hiroshima) ; Miao, Ying (J-HROSE-M2; Higashi-Hiroshima) Some constructions of semiframes.  ... 

Two classes of q-ary codes based on group divisible association schemes

Ying Miao, Sanpei Kageyama
1999 Discrete Mathematics  
If these block designs are further semiframes, another class of q-ary codes are also constructed.  ...  By means of Hall's Marriage Theorem, a class of q-ary codes are obtained through block designs based on group divisible association schemes with two associate classes.  ...  A portion of this work was carried out while Dr. Miao was a visiting scholar at the Faculty of School Education of Hiroshima University. The kind hospitality was gratefully acknowledged.  ... 
doi:10.1016/s0012-365x(98)00186-1 fatcat:qaolx6t2wjd63lcp663ffjadqe

Recursive constructions for cyclic quasiframes and cyclically resolvable cyclic Steiner 2-designs

Miwako Mishima, Masakazu Jimbo
2000 Discrete Mathematics  
In this paper, we will extend a semiframe to a more general notion 'quasiframe' and discuss a recursive construction for a quasiframe with cyclic property.  ...  Furthermore, as an application of a cyclic quasiframe, another recursive construction for a cyclically resolvable cyclic Steiner 2-design will be provided, which cannot be supplied by a recursive construction  ...  The authors also would like to thank the referees for their encouragement to improve readability of the paper.  ... 
doi:10.1016/s0012-365x(99)00141-7 fatcat:josrh5xnwzdbnhvgirjdji4amq

On Constructive Connectives and Systems

Arnon Avron, Ori Lahav, Martin Giese
2010 Logical Methods in Computer Science  
These results suggest new syntactic and semantic characterizations of basic constructive connectives.  ...  This general semantics is then used to provide a constructive (and very natural), sufficient and necessary coherence criterion for the validity of the strong cut-elimination theorem in such a system.  ...  A basic constructive connective is a connective defined by a set of rules in some coherent canonical system.  ... 
doi:10.2168/lmcs-6(4:12)2010 fatcat:4nwcnoc3hrf4va5mkoidn4yhci

Grooming for two-period optical networks

Charles J. Colbourn, Gaetano Quattrocchi, Violet R. Syrotiuk
2008 Networks  
This allows the two-period grooming problem to be expressed as an optimization problem on graph decompositions of K n that embed graph decompositions of K v for v ≤ n.  ...  In two-period optical networks, n vertices are required to support a grooming ratio of C in the first time period, while in the second time period a grooming ratio of C , C < C, is required for v ≤ n vertices  ...  Research of the authors is supported by MIUR-Italy (GQ) and NSF grant ANI-0240524 (VRS).  ... 
doi:10.1002/net.20252 fatcat:tr6arb62ljggrfrr6uqymfuuwa

The Space of Framed Functions

Kiyoshi Igusa
1987 Transactions of the American Mathematical Society  
There is however some ambiguity in the assignment of X to the function f.  ...  enough to choose an orthonormal basis for the tangent space of the cells e(x) at each of the critical points x of f.  ...  The deformation of I to g is given by (t(g2 + g3) + (1 -t)(f2 + 13)' 11)' 0 3. Semiframed functions. We introduce some intermediary spaces which lie between £b.(N) and fl!b.(N). DEFINITION 3.1.  ... 
doi:10.2307/2000654 fatcat:bfnthtxelfcqhiu7ecynsqe2ki

The space of framed functions

Kiyoshi Igusa
1987 Transactions of the American Mathematical Society  
There is however some ambiguity in the assignment of X to the function f.  ...  enough to choose an orthonormal basis for the tangent space of the cells e(x) at each of the critical points x of f.  ...  The deformation of I to g is given by (t(g2 + g3) + (1 -t)(f2 + 13)' 11)' 0 3. Semiframed functions. We introduce some intermediary spaces which lie between £b.(N) and fl!b.(N). DEFINITION 3.1.  ... 
doi:10.1090/s0002-9947-1987-0882699-7 fatcat:4loqpleb25honeicylgowclhpq

Page 36 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
In this paper we give some constructions for these designs and we also indicate some applications of these structures to the construction of other types of designs, e.g., incomplete group-divisible designs  ...  Summary: “A k-semiframe of type g“ is a group-divisible design (X, G, B) with parameters GD[{k}, {g}; gu] whose block set B can be written as a disjoint union B = PU Q,where P can be partitioned into parallel  ... 

Page 1330 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
We show that the rows of M can be extended to form an m x n’ rc-compact dyadic matrix which also preserves some of the properties of the matrix M.  ...  The proof of (2) uses (1), but the reviewer found it too sketchy to follow. (3) Call a set {K;} of (—1,0,1) matrices of order n a semiframe if it satisfies the conditions (ii) and (iii) of (1), as well  ... 

Kripke Semantics for Basic Sequent Systems [chapter]

Arnon Avron, Ori Lahav
2011 Lecture Notes in Computer Science  
This semantics is then used to obtain semantic characterizations of analytic sequent systems of this type, as well as of those admitting cut-admissibility.  ...  In particular, many well-known Kripke semantics for a variety of logics are easily obtained as special cases.  ...  Given an E-semiframe W, R, v , a signed formula of the form f:ψ (resp. t:ψ) is true in some world a ∈ W if ψ ∈ E and v(a, ψ) = f (v(a, ψ) = t). 3.  ... 
doi:10.1007/978-3-642-22119-4_6 fatcat:kdwokvz3dfgchfwy2mpyyvyuby

Canonical Constructive Systems [chapter]

Arnon Avron, Ori Lahav
2009 Lecture Notes in Computer Science  
We define the notions of a canonical inference rule and a canonical constructive system in the framework of strict single-conclusion Gentzen-type systems (or, equivalently, natural deduction systems),  ...  We show that every constructive canonical system induces a class of non-deterministic Kripke-style frames, for which it is strongly sound and complete.  ...  Here are some examples of well-known canonical rules: Conjunction.  ... 
doi:10.1007/978-3-642-02716-1_6 fatcat:qcysigafanfqnek35soqr3xqrq

Page 6633 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
If these block designs are further semiframes, another class of g-ary codes are also constructed.”  ...  As to interpretation, one may consider each r-partition as the exhaustive distribution of some character (or quality) to all the elements of some set Q, according to r viewpoints, the viewpoints forming  ... 

Page 7607 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
The authors introduce the notion of quasiframes as a general- ization of semiframes.  ...  At the time of publication there were some 25 entries which were open, i.e. the existence or nonexistence of D had not been determined. From 1983 until 1993 K. T.  ... 

Page 6490 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
Rees, Semiframes and nearframes (359-367); M. J. De Resmini, On the semifield plane of order 16 with kern GF(4) (369-390); D.  ...  Matveev, On the numerical solution of the ill-posed problems of construction of approximate solutions of singular integral equations of the second kind (88-92); I. V.  ... 
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