Complexity of two-variable Dependence Logic and IF-Logic

被引：4

作者：

Kontinen, Juha ^{[1
]}

Kuusisto, Antti ^{[2
]}

Lohmann, Peter ^{[3
]}

Virtema, Jonni ^{[2
]}

机构：

[1] Univ Helsinki, FIN-00014 Helsinki, Finland

[2] Univ Tampere, FIN-33101 Tampere, Finland

[3] Leibniz Univ Hannover, Hannover, Germany

来源：

26TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2011) | 2011年

基金：

芬兰科学院;

关键词：

dependence logic; independence-friendly logic; two-variable logic; decidability; complexity; satisfiability; expressivity; 1ST-ORDER LOGIC; 2; VARIABLES; QUANTIFIERS;

D O I：

10.1109/LICS.2011.14

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the two-variable fragments D-2 and IF2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D-2, both problems are NEXPTIME-complete, whereas for IF2, the problems are Pi(0)(1) and Sigma(0)(1)-complete, respectively. We also show that D-2 is strictly less expressive than IF2 and that already in D-2, equicardinality of two unary predicates and infinity can be expressed (the latter in the presence of a constant symbol). An extended version of this publication can be found at arxiv.org.

引用

页码：289 / 298

页数：10

共 50 条

[41] Domain-Lifted Sampling for Universal Two-Variable Logic and Extensions
Wang, Yuanhong
van Bremen, Timothy
Wang, Yuyi
Kuzelka, Ondrej
THIRTY-SIXTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE / THIRTY-FOURTH CONFERENCE ON INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE / TWELVETH SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE, 2022, : 10070 - 10079
[42] On Exact Sampling in the Two-Variable Fragment of First-Order Logic
Wang, Yuanhong
Pu, Juhua
Wang, Yuyi
Kuzelka, Ondrej
2023 38TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS, 2023,
[43] A simple combinatorial proof for the small model property of two-variable logic
Ma, Yanger
Tan, Tony
INFORMATION PROCESSING LETTERS, 2021, 170
[44] If-logic and truth-definition
Sandu G.
Journal of Philosophical Logic, 1998, 27 (2) : 143 - 164
[45] On Finite Satisfiability of Two-Variable First-Order Logic with Equivalence Relations
Kieronski, Emanuel
Tendera, Lidia
24TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, PROCEEDINGS, 2009, : 123 - +
[46] On the Expressive Power of IF-Logic with Classical Negation
Figueira, Santiago
Gorin, Daniel
Grimson, Rafael
LOGIC, LANGUAGE, INFORMATION AND COMPUTATION, WOLLIC 2011, 2011, 6642 : 135 - 145
[47] Extending Two-Variable Logic on Data Trees with Order on Data Values and Its Automata
Tan, Tony
ACM TRANSACTIONS ON COMPUTATIONAL LOGIC, 2014, 15 (01)
[48] Universal covers, color refinement, and two-variable counting logic: Lower bounds for the depth
Krebs, Andreas
Verbitsky, Oleg
2015 30TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS), 2015, : 689 - 700
[49] Complexity of the Two-Variable Fragment with Counting Quantifiers
Ian Pratt-Hartmann
Journal of Logic, Language and Information, 2005, 14 (3) : 369 - 395
[50] Complexity Results for Modal Dependence Logic
Lohmann, Peter
Vollmer, Heribert
STUDIA LOGICA, 2013, 101 (02) : 343 - 366

← 1 2 3 4 5 →