{"title":"Strong Backdoors for Default Logic","authors":"Johannes K. Fichte, Arne Meier, Irena Schindler","doi":"10.1145/3655024","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we introduce a notion of backdoors to Reiter’s propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor), for various kinds of target classes (CNF, KROM, MONOTONE) and all SCHAEFER classes. Also, we study generalisations of HORN-formulas, namely, QHORN, RHORN, as well as DUALHORN. For these classes, we also classify the computational complexity of the implication problem. We show that backdoor detection is fixed-parameter tractable for the considered target classes, and prove a complete trichotomy for backdoor evaluation. The problems are either fixed-parameter tractable, para-DeltaP2-complete, or para-NP-complete, depending on the target class.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computational Logic","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1145/3655024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce a notion of backdoors to Reiter’s propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor), for various kinds of target classes (CNF, KROM, MONOTONE) and all SCHAEFER classes. Also, we study generalisations of HORN-formulas, namely, QHORN, RHORN, as well as DUALHORN. For these classes, we also classify the computational complexity of the implication problem. We show that backdoor detection is fixed-parameter tractable for the considered target classes, and prove a complete trichotomy for backdoor evaluation. The problems are either fixed-parameter tractable, para-DeltaP2-complete, or para-NP-complete, depending on the target class.
期刊介绍：
TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. This area has a great tradition in computer science. Several researchers who earned the ACM Turing award have also contributed to this field, namely Edgar Codd (relational database systems), Stephen Cook (complexity of logical theories), Edsger W. Dijkstra, Robert W. Floyd, Tony Hoare, Amir Pnueli, Dana Scott, Edmond M. Clarke, Allen E. Emerson, and Joseph Sifakis (program logics, program derivation and verification, programming languages semantics), Robin Milner (interactive theorem proving, concurrency calculi, and functional programming), and John McCarthy (functional programming and logics in AI).
Logic continues to play an important role in computer science and has permeated several of its areas, including artificial intelligence, computational complexity, database systems, and programming languages.
The Editorial Board of this journal seeks and hopes to attract high-quality submissions in all the above-mentioned areas of computational logic so that TOCL becomes the standard reference in the field.
Both theoretical and applied papers are sought. Submissions showing novel use of logic in computer science are especially welcome.
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