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Small Substructures and Decidability Issues for First-Order Logic with Two Variables
20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
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We study first-order logic with two variables FO 2 and establish a small substructure property. ...
FO 2 here stands for the fragment of first-order logic with equality with only two variable symbols x and y, in finite relational vocabularies (without constants or function symbols). ...
We would like to thank the anonymous referees for their comments and criticism of an earlier version, which helped to improve the presentation. ...
doi:10.1109/lics.2005.49
dblp:conf/lics/KieronskiO05
fatcat:vlherolqgbcqbc6r4uksy7vahq
JSL volume 77 issue 3 Cover and Front matter
2012
Journal of Symbolic Logic (JSL)
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TABLE OF CONTENTS OF Small substructures and decidability issues for first-order logic with two variables, by EMANUEL KIERONSKI and MARTIN OTTO 729 A strong polarized relation, by SHIMON GARTI and SAHARON ...
for Dynamic Topological Logic, by
DAVID FERNANDEZ-DUQUE
947
Non-finitely axiomatisable two-dimensional modal logics, by AGI KURUCZ
and SERGIO MARCELINO
970
Non-genericity phenomena in ordered ...
doi:10.1017/s0022481200000463
fatcat:qy2zixdrf5dutd27w4622yngiq
Relational analysis of algebraic datatypes
2005
Proceedings of the 10th European software engineering conference held jointly with 13th ACM SIGSOFT international symposium on Foundations of software engineering - ESEC/FSE-13
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The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. ...
Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. ...
First-order logic with transitive closure. ...
doi:10.1145/1081706.1081740
dblp:conf/sigsoft/KuncakJ05
fatcat:22rzdy4s2zds7jx37vypheadsi
Relational analysis of algebraic datatypes
2005
Software engineering notes
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The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. ...
Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. ...
First-order logic with transitive closure. ...
doi:10.1145/1095430.1081740
fatcat:4kfwaivyqbb6xg4ufye3su775q
The Boundary Between Decidability and Undecidability for Transitive-Closure Logics
[chapter]
2004
Lecture Notes in Computer Science
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In this paper, we explore the boundary between decidability and undecidability for transitive-closure logics. ...
We also compare the complexity and expressibility of ∃∀(DTC + [E]) with related decidable languages including MSO(trees) and guarded fixed point logics. ...
Decidability of ∃∀(DTC + [E]) We start with the first-order logic ∃∀, consisting of first-order formulas in prenex form with all existential quantifiers preceding all universal quantifiers. ...
doi:10.1007/978-3-540-30124-0_15
fatcat:udyjqmt67ff45bvtxf6l6fj47y
On logics with two variables
1999
Theoretical Computer Science
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This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. ...
The decidability and complexity issues for modal and non-modal two-variables logics have been studied quite intensively in the last years. ...
Two-variable first-order with counting C2 extends F02 by allowing first-order counting quantifiers ZIGM, Slam , El="' for all m > 1. ...
doi:10.1016/s0304-3975(98)00308-9
fatcat:krqnks7mfbdyfamtm4m7swdkry
Decidable Expansions of Labelled Linear Orderings
2011
Logical Methods in Computer Science
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If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists a non-trivial expansion by a further monadic ...
Consider a linear ordering equipped with a finite sequence of monadic predicates. ...
The second author was partially supported by ESF project Games and EPSRC grant. ...
doi:10.2168/lmcs-7(2:5)2011
fatcat:emlw342vmza6jepks52olxiji4
One-Dimensional Guarded Fragments
2019
International Symposium on Mathematical Foundations of Computer Science
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two free variables need not be guarded, and which thus may be seen as a unification of GF and the two-variable fragment, FO 2 . ...
We call a first-order formula one-dimensional if every maximal block of existential (or universal) quantifiers in it leaves at most one variable free. ...
Acknowledgements The author would like to thank Sebastian Rudolph and the anonymous reviewers for their helpful comments. ...
doi:10.4230/lipics.mfcs.2019.16
dblp:conf/mfcs/Kieronski19
fatcat:h4yzat4tbfgythswdklitrcqf4
An Algebraic Glimpse at Bunched Implications and Separation Logic
[article]
2018
arXiv
pre-print
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We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics. ...
We propose generalized BI algebras (GBI-algebras) as a common framework for algebras arising via "declarative resource reading", intuitionistic generalizations of relation algebras and arrow logics and ...
Moreover, the second author wishes to thank: the family of the first author, in particular Julie Tapp, for hosting him for two weeks in April 2015, when the bulk of this paper was written; his project ...
arXiv:1709.07063v2
fatcat:mo56tyegqned5htws2wazhpphu
Decidable Expansions of Labelled Linear Orderings
[chapter]
2010
Lecture Notes in Computer Science
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We show that if A contains an interval of order type ω or −ω, and the monadic second-order theory of M is decidable, then there exists a non-trivial expansion M of M by a monadic predicate such that the ...
monadic second-order theory of M is still decidable. ...
The second author was partially supported by ESF project Games and EPSRC grant. ...
doi:10.1007/978-3-642-15025-8_5
fatcat:64n7ds34xzgnvmn5mcfb5rhjja
Margin-based first-order rule learning
2007
Machine Learning
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The implementation of the system includes plugins for logical queries, graphs and mathematical terms. ...
We present a new margin-based approach to first-order rule learning. ...
Due to its roots in first-order logic, most multi-relational rule learning algorithms are based on disjunctions or conjunctions of rules. ...
doi:10.1007/s10994-007-5034-6
fatcat:5e7fom236jdgxhy5yfzpim3mla
Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects
2011
The Journal of Artificial Intelligence Research
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We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited ...
at a fixed (small) domain size will necessarily extend to the general case. ...
Acknowledgments We would like to thank Umberto Grandi and three anonymous JAIR reviewers for a host of helpful comments and suggestions on earlier versions of this paper. ...
doi:10.1613/jair.3126
fatcat:l6tqox7f4zc6va53ctke3szrd4
Unary negation fragment with equivalence relations has the finite model property
[article]
2018
arXiv
pre-print
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We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. ...
We argue that the satisfiability (= finite satisfiability) problem for this logic is TwoExpTime-complete. ...
Acknowledgements This work is supported by Polish National Science Centre grant No 2016/21/B/ST6/01444. 2 We remark here that, since our normal form is one-dimensional, this is not possible for full ...
arXiv:1802.01318v2
fatcat:3nf73w32abh45dnm5zvcgrfe34
Yuri, Logic, and Computer Science
[chapter]
2010
Lecture Notes in Computer Science
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Algebra and Logic 8 (1969) , 640-642 (Russian) Consider the collection D of first-order formulas α such that the first-order theory with axiom α is decidable. ...
The classification of prefix-signature fragments of (first-order) predicate logic with equality, completed in [7] , is extended to first-order logic with equality and functions. ...
doi:10.1007/978-3-642-15025-8_1
fatcat:ehjpkiqxzbh55k7waxqwzfhw6y
Decidability of inferring inductive invariants
2016
Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016
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A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. ...
We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols. ...
Both TS and P will be encoded in first-order logic, and the encoding will be constructed such that the two correctness conditions hold: 1. ...
doi:10.1145/2837614.2837640
dblp:conf/popl/PadonISKS16
fatcat:mqryswehuzewnap62ehfb2lj2y
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