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Taming FirstOrder Logic
, 1998
"... In this paper we define computationally wellbehaved versions of classical firstorder logic and prove that the validity problem is decidable. ..."
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Cited by 2 (1 self)
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In this paper we define computationally wellbehaved versions of classical firstorder logic and prove that the validity problem is decidable.
The emergence of firstorder logic
 University of Minnesota Press, Minneapolis
, 1988
"... To most mathematical logicians working in the 1980s, firstorder logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on firstorder logic, it was ..."
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Cited by 4 (0 self)
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To most mathematical logicians working in the 1980s, firstorder logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on firstorder logic, it was
FirstOrder Logic of Proofs
, 2011
"... The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP capa ..."
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Cited by 27 (11 self)
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The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP
Computing With FirstOrder Logic
, 1995
"... We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtaine ..."
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Cited by 54 (13 self)
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We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results
Extended firstorder logic
, 2009
"... We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higherorder variables. We show that this fragment enjoys the characteristic properties of firstorder logic: complete proof systems, compactness, and c ..."
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Cited by 2 (1 self)
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We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higherorder variables. We show that this fragment enjoys the characteristic properties of firstorder logic: complete proof systems, compactness
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater ..."
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Cited by 316 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies
Indistinguishability and FirstOrder Logic
, 2008
"... The “richness” of properties that are indistinguishable from firstorder properties is investigated. Indistinguishability is a concept of equivalence among properties of combinatorial structures that is appropriate in the context of testability. All formulas in a restricted class of secondorder log ..."
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logic are shown to be indistinguishable from firstorder formulas. Arbitrarily hard properties, including REcomplete properties, that are indistinguishable from firstorder formulas are shown to exist. Implications on the search for a logical characterization of the testable properties are discussed.
FirstOrder Logical Duality
, 2008
"... Generalizing Stone duality for Boolean algebras, an adjunction between Boolean coherent categories—representing firstorder syntax—and certain topological groupoids—representing semantics—is constructed. The embedding of a Boolean algebra into a frame of open sets of a space of 2valued models is re ..."
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Cited by 14 (4 self)
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of the equivalence between Boolean algebras and Stone spaces consist of ‘homming into 2’. By slicing over this groupoid (modified to display an alternative setup), Chapter 3 shows how the adjunction specializes to the case of firstorder single sorted logic to yield an adjunction between such theories
Undecidability of FirstOrder Logic
"... 2.1 A signature for lines............................... 6 ..."
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