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Two-Variable Logic with Two Order Relations
2012
Logical Methods in Computer Science
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As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. ...
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary ...
We thank Jan van den Bussche for fruitful discussions and Amaldev Manuel for sharing his results with us. ...
doi:10.2168/lmcs-8(1:15)2012
fatcat:j5m6amxmwraihghwy76ej3tzhm
Two-Variable Logic with Two Order Relations
[chapter]
2010
Lecture Notes in Computer Science
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As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. ...
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary ...
TWO-VARIABLE LOGIC WITH TWO ORDER RELATIONS 3 Results. ...
doi:10.1007/978-3-642-15205-4_38
fatcat:cfgr6ldxcrczhpthxhexxzq74i
Satisfiability for two-variable logic with two successor relations on finite linear orders
[article]
2013
arXiv
pre-print
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We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. ...
We study the two variable fragment of first-order logic with two variables and two successor relations on two finite linear orders. We show that the problem is decidable in NExpTime. ...
a non-primitive-recursive algorithm. 2 Our result also trivially extends to the satisfiability of existential monadic second order logic with two variables (EMSO 2 ) and two successor relations on finite ...
arXiv:1204.2495v3
fatcat:hvc3msmleff4dbcmthkvfhttnq
The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable
[article]
2017
arXiv
pre-print
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We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. ...
The finite satisfiability problem for this logic is shown to be decidable, in triply exponential non-deterministic time. ...
Introduction The two-variable fragment, henceforth denoted L 2 , is the fragment of firstorder logic with equality but without function-symbols, in which only two logical variables may appear. ...
arXiv:1707.05558v1
fatcat:dcll44gbyrfqtdrfyogovdyame
On Spatial Conjunction as Second-Order Logic
[article]
2004
arXiv
pre-print
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form of second-order quantification in two-variable logic is decidable. ...
We construct an embedding from first-order logic with spatial conjunction into second-order logic, and more surprisingly, an embedding from full second order logic into first-order logic with spatial conjunction ...
The consequences of the translation from second-order logic to spatial conjunction for two-variable logic with counting were crystallized in discussion with Greta Yorsh. ...
arXiv:cs/0410073v1
fatcat:ezlx6bafgzb5veyhymdgqr2rne
The Expressive Power of Two-Variable Least Fixed-Point Logics
[chapter]
2005
Lecture Notes in Computer Science
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The two-variable fragment of binary least fixed-point logic with parameters is strictly more expressive than the two-variable fragment of monadic least fixed-point logic with parameters (even on finite ...
The two-variable fragment of monadic least fixed-point logic with parameters is as expressive as full monadic least fixed-point logic (on binary structures). 2. ...
In this paper we deal primarily with two-variable logics -logics that only allow for two distinct first-order variables. ...
doi:10.1007/11549345_37
fatcat:ixiptx4ryrcinj626g4nuovyyu
Undecidability of First-Order Intuitionistic and Modal Logics with Two variables
2005
Bulletin of Symbolic Logic
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We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors ...
We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. ...
Two-variable first-order modal logics with expanding domains. ...
doi:10.2178/bsl/1122038996
fatcat:h5uopao7freuza6buw76iwm4fm
The Logic of Counterpart Theory with Actuality
2012
Journal of Philosophical Logic
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We argue that these claims are not based on logical flaws of counterpart theory itself, but point to the lack of appropriate devices in first-order logic for "remembering" the values of variables. ...
We formulate a mildly dynamic version of first-order logic with appropriate memory devices and show how to base a version of counterpart theory with actuality on this. ...
To capture this difference in two-dimensional first-order logic, we introduce two sorts of variables. ...
doi:10.1007/s10992-012-9248-0
fatcat:kyau36tggrdu7pu7iznimsq4aa
Monodic Fragments of First-Order Temporal Logics: 2000–2001 A.D
[chapter]
2001
Lecture Notes in Computer Science
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Outline of talk Most propositional temporal logics are decidable. But the decision problem in predicate (first-order) temporal logics has seemed near-hopeless. ...
Example Over N, even with only 2 variables and unary relation symbols, predicate temporal logic is • undecidable, • not recursively axiomatisable. ...
Complexity Seems to be MAX(EXPSPACE, complexity of underlying first-order fragment). • Monodic one-variable, (two-variable too?) ...
doi:10.1007/3-540-45653-8_1
fatcat:pqavraufgva2vl6icvm7om6yby
Relation Algebra with Binders
2001
Journal of Logic and Computation
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The language of relation algebras is expanded with variables denoting individual elements in the domain and with the binder from hybrid logic. ...
Every elementary property of binary relations is expressible in the resulting language, something which fails for the relation algebraic language. ...
, awarded by the Dutch Research Council NWO to the Dutch research School in Logic. ...
doi:10.1093/logcom/11.5.691
fatcat:a2rdoavhcbc77du2tn3wki5rva
Learning directed probabilistic logical models: ordering-search versus structure-search
2008
Annals of Mathematics and Artificial Intelligence
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We discuss how to learn non-recursive directed probabilistic logical models from relational data. ...
We experimentally compare the two upgraded algorithms on two relational domains. ...
Second, we experimentally compare the resulting algorithm with the upgraded structure-search algorithm on two relational domains. ...
doi:10.1007/s10472-009-9134-9
fatcat:pt5zatdj3rcb3biyyabrgv3any
The relation between logic and functional languages: a survey
1986
The Journal of Logic Programming
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of two terms, possibly containing quantified) variables. ...
LEAF [2, 3] , which has lazy evaluation of relations too. The partial ordering is defined by annotating variables also in the relational atoms. ...
In the case of first-order logic programming, this need has led to the language-metalanguage amalgamation proposal [lo, 111, which is less powerful than higher-order logic and sometimes rather difficult ...
doi:10.1016/0743-1066(86)90014-2
fatcat:kzu7tvyz2fajvlsl767fgczjfe
Modal Foundations for Predicate Logic
1997
Logic Journal of the IGPL
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Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. ...
The complexity of any logical modeling re ects both the intrinsic structure of a topic described and the weight of the formal tools. ...
With only two variables, the latter information applied to the variable y says that ; are related via some nite sequence (possibly empty) of R x -steps. ...
doi:10.1093/jigpal/5.2.259
fatcat:s4rwxtwym5aednxwo5cazrj6ba
Propositional Quantification in Bimodal $$\mathbf {S5}$$S5
2018
Erkenntnis: An International Journal of Scientific Philosophy
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It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. ...
The embedding is then extended to all sublogics containing the logic of so-called fusions of frames with equivalence relations. ...
(d 1 ) (d 2 ) ⋮ D D d e (e) d, (e) To make this idea precise, associate, injectively, each first-order variable x with a propositional variable p x and each binary second-order variable X with a propositional ...
doi:10.1007/s10670-018-0035-3
fatcat:jagbf3vpabcvznut6esbqtfcvy
Finite models and finitely many variables
1999
Banach Center Publications
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This paper is a survey of results on finite variable logics in finite model theory. It focusses on the common underlying techniques that unite many such results. ...
The two logics in question are dynamic logics formed from program schemes with one stack (LFDS) and program schemes with arrays (LPDA). ...
To be precise, the logic LFP is obtained by closing first order logic under the following formula formation rule: If ϕ is a formula, R an l-ary relational variable occurring only positively in ϕ,x is an ...
doi:10.4064/-46-1-93-117
fatcat:uaadzrnjyzavpkkqcrsqpahoca
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