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Small Substructures and Decidability Issues for First-Order Logic with Two Variables

E. Kieronski, M. Otto
20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)  
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)  
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

Viktor Kuncak, Daniel Jackson
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  
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

Viktor Kuncak, Daniel Jackson
2005 Software engineering notes  
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]

Neil Immerman, Alex Rabinovich, Tom Reps, Mooly Sagiv, Greta Yorsh
2004 Lecture Notes in Computer Science  
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

Erich Grädel, Martin Otto
1999 Theoretical Computer Science  
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

Alexis Bès, Alexander Rabinovich, Bruno Courcelle
2011 Logical Methods in Computer Science  
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

Emanuel Kieronski, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
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]

Peter Jipsen, Tadeusz Litak
2018 arXiv   pre-print
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]

Alexis Bès, Alexander Rabinovich
2010 Lecture Notes in Computer Science  
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

Ulrich Rückert, Stefan Kramer
2007 Machine Learning  
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

C. Geist, U. Endriss
2011 The Journal of Artificial Intelligence Research  
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]

Daniel Danielski, Emanuel Kieronski
2018 arXiv   pre-print
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]

Andreas Blass, Nachum Dershowitz, Wolfgang Reisig
2010 Lecture Notes in Computer Science  
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

Oded Padon, Neil Immerman, Sharon Shoham, Aleksandr Karbyshev, Mooly Sagiv
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
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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