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### Two-Variable Logic with Two Order Relations

Thomas Schwentick, Thomas Zeume, Anuj Dawar
2012 Logical Methods in Computer Science
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.  ...

### Two-Variable Logic with Two Order Relations [chapter]

Thomas Schwentick, Thomas Zeume
2010 Lecture Notes in Computer Science
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.  ...

### Satisfiability for two-variable logic with two successor relations on finite linear orders [article]

Diego Figueira
2013 arXiv   pre-print
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  ...

### The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable [article]

Ian Pratt-Hartmann
2017 arXiv   pre-print
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.  ...

### On Spatial Conjunction as Second-Order Logic [article]

Viktor Kuncak, Martin Rinard
2004 arXiv   pre-print
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.  ...

### The Expressive Power of Two-Variable Least Fixed-Point Logics [chapter]

Martin Grohe, Stephan Kreutzer, Nicole Schweikardt
2005 Lecture Notes in Computer Science
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.  ...

### Undecidability of First-Order Intuitionistic and Modal Logics with Two variables

Roman Kontchakov, Agi Kurucz, Michael Zakharyaschev
2005 Bulletin of Symbolic Logic
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.  ...

### The Logic of Counterpart Theory with Actuality

2012 Journal of Philosophical Logic
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.  ...

### Monodic Fragments of First-Order Temporal Logics: 2000–2001 A.D [chapter]

Ian Hodkinson, Frank Wolter, Michael Zakharyaschev
2001 Lecture Notes in Computer Science
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?)  ...

### Relation Algebra with Binders

M. Marx
2001 Journal of Logic and Computation
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.  ...

### Learning directed probabilistic logical models: ordering-search versus structure-search

Daan Fierens, Jan Ramon, Maurice Bruynooghe, Hendrik Blockeel
2008 Annals of Mathematics and Artificial Intelligence
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.  ...

### The relation between logic and functional languages: a survey

Marco Bellia, Giorgio Levi
1986 The Journal of Logic Programming
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  ...

### Modal Foundations for Predicate Logic

J. van Benthem
1997 Logic Journal of the IGPL
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.  ...

### Propositional Quantification in Bimodal $$\mathbf {S5}$$S5

Peter Fritz
2018 Erkenntnis: An International Journal of Scientific Philosophy
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  ...

### Finite models and finitely many variables

Anuj Dawar
1999 Banach Center Publications
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  ...
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