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Keywords
(1)
Linear Logic
Related Publications
(7)
Investigations into logical deduction
ThreeValued Logics for Inconsistency Handling
Encoding Logical Theories of Programs
On the complexity of Entailment in Propositional Multivalued Logics
Reasoning with Logical Bilattices
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Simple Consequence Relations
Simple Consequence Relations,10.1016/08905401(91)90023U,Information and Computation/information and Control,Arnon Avron
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Simple Consequence Relations
(
Citations: 93
)
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Arnon Avron
We provide a general investigation of Logic in which the notion ofa simple consequence relation is taken to be fundamental. Our notionis more general than the usual one since we give up monotonicityand use multisets rather than sets. We use our notion for characterizingseveral known logics (including
Linear Logic
and nonmonotoniclogics) and for a general, semanticsindependent classification of standardconnectives via equations on consequence relations (these includeGirard's...
Journal:
Information and Computation/information and Control  IANDC
, vol. 92, no. 1, pp. 105140, 1991
DOI:
10.1016/08905401(91)90023U
Cumulative
Annual
Citation Context
(44)
...The rule should also be pure in the sense of [
1
] (i.e...
Arnon Avron
,
et al.
Strict Canonical Constructive Systems
...notion of (abstract) consequence relation has been formalised by Gentzen, Tarski and Scott [
2
,22,45]...
...A generalisation by Avron [
2
] also allows for inclusion of substructural (e.g., nonmonotonic) logics...
...1 More general notions work with multisets instead of sets of premises [
2
]...
...Note that our definition of negation also covers intuitionistic negation (unlike the treatment in [
2
], which assumes ¬¬elimination)...
...A theory Γ ⊆ S is satisfiable ,i f it has am odelM (i.e., a model M ∈M such that M = ϕ for ϕ ∈ Γ). Semantic entailment in a room is defined as usual: for Γ ⊆ S and ϕ ∈ S, we write Γ = ϕ, if all models satisfying all sentences in Γ also satisfy ϕ. The following result is folklore [
2
]:...
...What happens then when we change the set of propositional symbols? For example [
2
,3] mention the property of an entailment relation to be stable under mappings of the propositional variables...
Till Mossakowski
,
et al.
What is a Logic Translation?
...The rule should also be pure in the sense of [
1
] (i.e., there should be no side conditions limiting its application), and its active formulas should be immediate subformulas of its principal formula...
Arnon Avron
,
et al.
Canonical Constructive Systems
...However, it rules out from the class of “logics in L” just two trivial logics (see [7]), and it is technically convenient to include it. 5 See [
1
] for the differences between the “truth” and “validity” consequence relations of...
Arnon Avron
.
Multivalued Semantics: Why and How
...All rule systems representable in LF satisfy the structural properties of a hypothetical judgement (weakening, exchange, contraction, and substitution) because all LF rules are pure [
4
]—they place no constraints on the context in which they can be applied...
Daniel R. LicataNoam
,
et al.
Focusing on Binding and Computation
References
(24)
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Published in 1977.
A Short Introduction to Modal Logic
(
Citations: 21
)
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Published in 1992.
Introduction to mathematical logic
(
Citations: 719
)
E. Mendelson
Published in 1964.
A Framework for Defining Logics
(
Citations: 727
)
Robert Harper
,
Furio Honsell
,
Gordon D. Plotkin
Conference:
Logic in Computer Science  LICS
, pp. 194204, 1987
What Is an Inference Rule?
(
Citations: 20
)
Ronald Fagin
,
Joseph Y. Halpern
,
Moshe Y. Vardi
Journal:
Journal of Symbolic Logic  JSYML
, vol. 57, no. 3, pp. 10181045, 1992
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Citations
(93)
Deductive coherence and norm adoption
(
Citations: 2
)
Sindhu Joseph
,
Carles Sierra
,
W. Marco Schorlemmer
,
Pilar Dellunde
Journal:
Logic Journal of The Igpl / Bulletin of The Igpl  IGPL
, vol. 18, no. 1, pp. 118156, 2010
Strict Canonical Constructive Systems
(
Citations: 2
)
Arnon Avron
,
Ori Lahav
Conference:
Birthday ...
, pp. 7594, 2010
The proof monad
(
Citations: 1
)
Florent Kirchner
,
César Muñoz
Journal:
The Journal of Logic and Algebraic Programming  JLP
, vol. 79, no. 35, pp. 264277, 2010
What is a Logic Translation?
(
Citations: 6
)
Till Mossakowski
,
Răzvan Diaconescu
,
Andrzej Tarlecki
Journal:
Logica Universalis
, vol. 3, no. 1, pp. 95124, 2009
Canonical Constructive Systems
(
Citations: 3
)
Arnon Avron
,
Ori Lahav
Conference:
Analytic Tableaux and Related Methods  TABLEAUX
, pp. 6276, 2009