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Structural Extensions of Display Calculi: A General Recipe
[chapter]
2013
Lecture Notes in Computer Science
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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
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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
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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
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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
2010
Electronic Proceedings in Theoretical Computer Science
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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
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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
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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]
1996
arXiv
pre-print
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[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]
1997
arXiv
pre-print
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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
1997
Banach Center Publications
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[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
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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
1999
Theoretical Computer Science
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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
1998
Journal of Geometry and Physics
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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
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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
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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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