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Logic with Equality: Partisan Corroboration and Shifted Pairing

Yuri Gurevich, Margus Veanes
1999 Information and Computation  
In the presence of equality, which is the case in this paper, this problem was recently shown to be undecidable. The main contributions of this paper are two theorems.  ...  of intuitionistic logic with equality. ] 1999 Academic Press Article ID inco.1999.2797, available online at http:ÂÂ on 205 0890-5401Â99 30.00 Any syntactic object is ground if it contains  ...  We thank Florent Jacquemard for useful comments on a preliminary version of this paper. The comments and suggestions of an anonymous referee greatly improved the final manuscript.  ... 
doi:10.1006/inco.1999.2797 fatcat:ilro4ckdlzexpcjv7ina2k6xmu

Horn Fragments of the Halpern-Shoham Interval Temporal Logic

Davide Bresolin, Agi Kurucz, Emilio Muñoz-Velasco, Vladislav Ryzhikov, Guido Sciavicco, Michael Zakharyaschev
2017 ACM Transactions on Computational Logic  
Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.  ...  We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying  ...  This allows us to use ⟨R⟩ on the left-hand side of the clauses in HS ✷ horn -formulas, and [R] on the right-hand side of the clauses in HS ✸ horn -formulas.  ... 
doi:10.1145/3105909 fatcat:t3usanf765fxxhr3ximldikmy4

eThor: Practical and Provably Sound Static Analysis of Ethereum Smart Contracts [article]

Clara Schneidewind, Ilya Grishchenko, Markus Scherer, Matteo Maffei
2020 arXiv   pre-print
In this work, we present eThor, the first sound and automated static analyzer for EVM bytecode, which is based on an abstraction of the EVM bytecode semantics based on Horn clauses.  ...  static analyzers: specifically, eThor is the only one to provide soundness guarantees, terminates on 95% of a representative set of real-world contracts, and achieves an F-measure (which combines sensitivity  ...  and implementation of static analyses based on Horn clause resolution.  ... 
arXiv:2005.06227v1 fatcat:fyo2hk6uzbd3rjkhlwno3osa4m

A Road Map of Interval Temporal Logics and Duration Calculi

Valentin Goranko, Angelo Montanari, Guido Sciavicco
2004 Journal of Applied Non-Classical Logics  
We survey main developments, results, and open problems on interval temporal logics and duration calculi.  ...  We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.  ...  Science and Technology Agreement, that they have received for the project: "Theory and applications of temporal logics to computer science and artificial intelligence".  ... 
doi:10.3166/jancl.14.9-54 fatcat:svndmwuu6jex5mvhpvslv74v6m

Queries with negation and inequalities over lightweight ontologies

Víctor Gutiérrez-Basulto, Yazmín Ibáñez-García, Roman Kontchakov, Egor V. Kostylev
2015 Journal of Web Semantics  
We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable.  ...  Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and EL families.  ...  Recall that the proof is by reduction of the complement of Horn-3SAT, the satisfiability problem for Horn clauses with at most three literals.  ... 
doi:10.1016/j.websem.2015.06.002 fatcat:4tzjioy3ung7djkunzjmguruwy

Computational Complexity of Deciding Provability in Linear Logic and its Fragments [article]

Florian Chudigiewitsch
2021 arXiv   pre-print
A central problem of the logic is the question whether a given list of formulas is provable with the calculus.  ...  In the research regarding the complexity of this problem, some results were achieved, but other questions are still open.  ...  We define and-branching two counter machines and show that the halting problem for two counter machines with zero tests, which is known to be undecidable, can be reduced to their halting problem. .  ... 
arXiv:2110.00562v1 fatcat:a6sidawnbjh5jpf2cvrermfrcy

Verification of Imperative Programs by Constraint Logic Program Transformation

Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi, Maurizio Proietti
2013 Electronic Proceedings in Theoretical Computer Science  
Since the problem is undecidable, this process may not terminate.  ...  (and in this case prog is not correct), or by (ii) the empty set of clauses (and in this case prog is correct).  ...  We would like to thank Anindya Banerjee, Olivier Danvy, Kyung-Goo Doh, and John Hatcliff for their kind invitation to contribute to this symposium in honor of Dave Schmidt.  ... 
doi:10.4204/eptcs.129.12 fatcat:ot54j7sol5errm7cryxolqywcy

HiLog: A foundation for higher-order logic programming

Weidong Chen, Michael Kifer, David S. Warren
1993 The Journal of Logic Programming  
For example, Prolog combines predicate calculus, higher-order, and meta-level programming in one working system, allowing programmers routine use of generic predicate definitions (e.g., transitive closure  ...  Another well-known useful feature is the "call" meta-predicate of Prolog. Applications of higher-order constructs in the database context have been pointed out in many works, including [24, 29, 411.  ...  When it = 0, a clause is called the empty clause. A Horn clause is a clause that contains at most one positive literal. A definite clause is a Horn clause of the form A V 7' B, V . . .  ... 
doi:10.1016/0743-1066(93)90039-j fatcat:ijjkcjymbje43mbiacp6ogkswm

Towards Formal Verification of Role-Based Access Control Policies

S. Jha, Ninghui Li, M. Tripunitara, Qihua Wang, W. Winsborough
2008 IEEE Transactions on Dependable and Secure Computing  
In this paper, we formalize classes of security analysis problems in the context of Role-Based Access Control. We show that in general, these problems are PSPACE-complete.  ...  We also study the factors that contribute to the computational complexity by considering a lattice of various subcases of the problem with different restrictions.  ...  Each initial role membership of the user can be translated into a Horn clause. The query can be translated into a Horn query clause.  ... 
doi:10.1109/tdsc.2007.70225 fatcat:osup3kqctzdjtm2acjkty37xba

Ontological Query Answering with Existential Rules [chapter]

Marie-Laure Mugnier
2011 Lecture Notes in Computer Science  
We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account.  ...  To tackle this problem, we consider a logical framework based on existential rules, also called Tuple-Generating Dependencies or Datalog+/-rules. This framework can also be defined in graph terms.  ...  The author thanks Sebastian Rudolph for his careful reading of this paper and helpful comments.  ... 
doi:10.1007/978-3-642-23580-1_2 fatcat:tv247xwuofb2lcqavb6snjpl2e

The expressivity of universal timed CCP

Carlos Olarte, Frank D. Valencia
2008 Proceedings of the 10th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '08  
The encoding uses a monadic constraint system allowing us to prove a new result for a fragment of FLTL: The undecidability of the validity problem for monadic FLTL without equality and function symbols  ...  It also justifies the restriction imposed in previous decidability results on the quantification of flexible-variables.  ...  Basically, in [2] protocols are modeled as a set of Horn clauses rather than processes.  ... 
doi:10.1145/1389449.1389452 dblp:conf/ppdp/OlarteV08 fatcat:q7u44rkkvfgxbfvybltdqtj7ve

Subject index volumes 1–200

1999 Theoretical Computer Science  
defined by Horn clauses, 862 dynamic -, 2297 equational -, 2035,2147,2372,2541.2748 extended -. 2035 for processes, 30 I2 Horn clause -. 2295 logical -. 2074 theories of bounded concatenation  ...  tree automata, 3275 undecidability of the 3 -fragment of intuitionistic logic with equality, 3295 halting problem, 1723 inclusion problem, 30, 3491 second-order unification problem, 1620 simplification  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

On rules with existential variables: Walking the decidability line

Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, Eric Salvat
2011 Artificial Intelligence  
Then, we study the question of whether the union of two decidable classes remains decidable and show that the answer is negative, except for one class and a still open case.  ...  Previous known decidable classes were based on forward chaining. On the one hand we extend these classes, on the other hand we introduce decidable classes based on backward chaining.  ...  Acknowledgements We thank Georg Gottlob for the reference to [37] , Michaël Thomazo for his careful reading of a previous version of this paper, as well as the anonymous reviewers for their relevant and  ... 
doi:10.1016/j.artint.2011.03.002 fatcat:pi5onanwwjhzdof67f7nshf6yi

Querying Log Data with Metric Temporal Logic (Technical Report) [article]

Sebastian Brandt, Elem Güzel Kalaycı, Vladislav Ryzhikov, Guohui Xiao, Michael Zakharyaschev
2018 arXiv   pre-print
We propose a novel framework for ontology-based access to temporal log data using a datalog extension datalogMTL of a Horn fragment of the metric temporal logic MTL.  ...  We show that datalogMTL is ExpSpace-complete even with punctual intervals, in which case full MTL is known to be undecidable.  ...  Guohui Xiao is the corresponding author of this article.  ... 
arXiv:1703.08982v3 fatcat:qjyvrtzy6fgzhkfcmibjroan44

Termination of logic programs: the never-ending story

Danny de Schreye, Stefaan Decorte
1994 The Journal of Logic Programming  
At this point, we justify the title by presenting an extensive survey on: Termination of Logic Programs: the Never-Ending Story (see tirst page).  ...  Apt Martens for proofreading drafts of the paper, to K. Verschaetse for allowing us to adapt a few paragraphs from his Ph.D., and to C. Hogger for inspiring the title.  ...  Therefore, they inherit the undecidability of the halting problem for Turing machines.  ... 
doi:10.1016/0743-1066(94)90027-2 fatcat:ukeksb2uzjdnpddgp52hgrnp6a
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