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» Definability in Logic and Rough Set Theory
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KR
2000
Springer
13 years 11 months ago
Reasoning with Axioms: Theory and Practice
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to a...
Ian Horrocks, Stephan Tobies
FUIN
2010
83views more  FUIN 2010»
13 years 4 months ago
Expressing Cardinality Quantifiers in Monadic Second-Order Logic over Trees
We study an extension of monadic second-order logic of order with the uncountability quantifier "there exist uncountably many sets". We prove that, over the class of fini...
Vince Bárány, Lukasz Kaiser, Alexand...
CORR
2008
Springer
148views Education» more  CORR 2008»
13 years 6 months ago
Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems--such as for ...
Guillaume Burel
20
Voted
MLQ
2006
78views more  MLQ 2006»
13 years 7 months ago
Recursive logic frames
We define the concept of a logic frame, which extends the concept stract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the...
Saharon Shelah, Jouko A. Väänänen
IGPL
2008
124views more  IGPL 2008»
13 years 7 months ago
The Ricean Objection: An Analogue of Rice's Theorem for First-order Theories
We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order t...
Igor Carboni Oliveira, Walter Alexandre Carnielli