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Structural Extensions of Display Calculi: A General Recipe [chapter]

Agata Ciabattoni, Revantha Ramanayake
2013 Lecture Notes in Computer Science  
We present a systematic procedure for constructing cut-free display calculi for axiomatic extensions of a logic via structural rule extensions.  ...  As a case study, we present cut-free calculi for extensions of well-known logics including Bi-intuitionistic and tense logic.  ...  All the above results start with a specific logic and introduce calculi for (some of) its axiomatic extensions, e.g., Full Lambek calculus with exchange FLe for [5, 6] , or the tense logic Kt for [14  ... 
doi:10.1007/978-3-642-39992-3_10 fatcat:nldyzckvi5a6fdxjci55qw7uy4

Page 1102 of Mathematical Reviews Vol. 51, Issue 4 [page]

1976 Mathematical Reviews  
William, Jr. 7850 Translations and structure for partial propositional calculi. Studia Logica 33 (1974), 35-57.  ...  will be answered for increasingly detailed versions of structure.” {It seems to the reviewer that some ideas and results of this paper can profitably be extended to modal propositional logics.} N. C.  ... 

Page 445 of Mathematical Reviews Vol. 33, Issue 3 [page]

1967 Mathematical Reviews  
Fenstad (Blindern) Harrop, Ronald Some structure results for propositional calculi. J. Symbolic Logic 30 (1965), 271-292.  ...  (2) Are there structural criteria for determining of a given propositional calculus whether or not it has both decidable and undecidable extensions ?  ... 

Page 1827 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
The initial vehicle for the exploration is a model-thecretic structure, RM3?  ...  The constraints are weak enough to allow {p: a believes p at 7} to be inconsistent, and to contain analytically false propositions, but strong enough to impose some logical structure on an agent’s beliefs  ... 

A criterion for separating process calculi

Federico Banti, Rosario Pugliese, Francesco Tiezzi
2010 Electronic Proceedings in Theoretical Computer Science  
As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that  ...  priority and from mainstream calculi.  ...  We thank Daniele Gorla and the anonymous reviewers for their fruitful comments that have helped us in improving the paper.  ... 
doi:10.4204/eptcs.41.2 fatcat:f2fifmdomrhwnbl7vanrnedcca

Page 595 of Mathematical Reviews Vol. 41, Issue 3 [page]

1971 Mathematical Reviews  
The author proves the completeness theorem for the systems of m-valued predicate calculi of first order based on the m-valued propositional calculi of G. Rousseau.  ...  and intuitionistic n-valued propositional calculi are constructed.  ... 

Page 4293 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
Chapter 8 is devoted to an excellent and long analysis of fuzzy calculi, considering that fuzzy calculi provide, in some measure, a  ...  The tree method for finite n- valued propositional calculi is algorithmic and its use for the predicate calculus requires certain refinements, as the authors show.  ... 

First Order Calculi with Values in Right--Universal Bimodules [article]

A. Borowiec, V. K. Kharchenko, Z. Oziewicz
1996 arXiv   pre-print
[1990] and that in this language results are in a natural context, are easier to describe and handle.  ...  As a by--product we obtained intrinsic, coordinate--free and basis--independent generalization of the first order noncommutative differential calculi with partial derivatives.  ...  Combining Proposition 1.2.1 with the results above we have R e m a r k 2.  ... 
arXiv:q-alg/9609010v1 fatcat:ubyfxgknjrgkjp7dzvajigdiku

Advances in Quantum and Braided Geometry [article]

S. Majid
1997 arXiv   pre-print
We demonstrate our recent general results on the Casimir construction and moduli space of all bicovariant calculi by means of some detailed examples, including finite-difference and 2-jet cacluli on ^n  ...  Brzezinski of quantum group gauge theory with examples of such nonuniversal differential calculi on spacetime. We outline a notion of quantum homotopy of a quantum space.  ...  Dobrev and other members of the organising committee for an excellent conference Group XXI in Goslar.  ... 
arXiv:q-alg/9610003v2 fatcat:zsxo52myujgifk765mfl5qb7ii

First order calculi with values in right-universal bimodules

Andrzej Borowiec, Vladislav Kharchenko, Zbigniew Oziewicz
1997 Banach Center Publications  
[1990] and that in this language results are in a natural context, are easier to describe and handle.  ...  As a by-product we obtain intrinsic, coordinate-free and basisindependent generalization of the first order noncommutative differential calculi with partial derivatives.  ...  Some of the results below are valid in the general situation T V /I. Some other, require an additional assumption that V ⊆ T V /I .  ... 
doi:10.4064/-40-1-171-184 fatcat:yqwxeucemfap3cxsopfce63cmu

Page 13 of Mathematical Reviews Vol. 50, Issue 1 [page]

1975 Mathematical Reviews  
Tokarz [same Studia 32 (1973), 77-91; MR 49 #8850] defined and studied several different kinds of “completeness” for struc- tural propositional calculi, including ‘Post completeness”, “maximality”, “‘structural  ...  He gives a very general definition of a “semantics” for any system of logic, and obtains some negative results: in particular, decidability does not imply compactness, nor does compactness imply recursive  ... 

Closed action calculi

Philippa Gardner
1999 Theoretical Computer Science  
Our results show that in some sense names are inessential. However, the purpose of action calculi is to understand formalisms which mimic the behaviour of interactive systems.  ...  Action calculi provide a framework for capturing many kinds of interactive behaviour by focussing on the primitive notion of names.  ...  Acknowledgements My thanks go to Robin Milner for his encouragement and many interesting discussions regarding this work, and to Masahito Hasegawa for his comments on a previous draft.  ... 
doi:10.1016/s0304-3975(98)00355-7 fatcat:nhkttwu6n5c75dgtj5idk3noui

Classification of bicovariant differential calculi

S. Majid
1998 Journal of Geometry and Physics  
For a classical Lie group we obtain an in nite family of nonstandard calculi. General constructions for bicovariant calculi and their quantum tangent spaces are also obtained.  ...  We show that the bicovariant rst order di erential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations V of the quantum group enveloping algebra  ...  We conclude the section with some general constructions for bicovariant calculi and their quantum tangent spaces.  ... 
doi:10.1016/s0393-0440(97)00025-9 fatcat:npw57xjwjbaqlbto6nfnz74jvq

Page 1571 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
The investigations of these logical systems are enriched by complexity and undecidability results for propositional as well as for first-order systems.  ...  The main result of our paper is that a (propositional) sequent consequence (in Tarski’s sense) sat- isfies weak structural rules, that is, structural rules with Cut split into two weaker rules typical  ... 

Page 4077 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
The results obtained in the present paper contrast sharply with the finite axiomatizability results for many other second-order intuitionistic propositional logics.  ...  4077 Now, let Hj be the second-order intuitionistic propositional logic characterized by all principal Kripke structures, i.e., the set of all formulas valid in every principal Kripke structure.  ... 
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