A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4
@article{Cerrito1997APT, title={A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4}, author={Serenella Cerrito and Marta Cialdea Mayer}, journal={Log. J. IGPL}, year={1997}, volume={5}, pages={287-300} }
The concern of this paper is the study of automated deduction methods for propositional modal logics. We use tableau proof-systems to show that Fitting's translation of the transitive modal logic S4 into T can be constructed in deterministic polynomial time. This result is exploited in order to establish a polynomial bound to the length of branches in both tableau and sequent proof search for the transitive logics S4 and K4. This allows the elimination of \periodicity tests" when proving S4…
19 Citations
Single Step Tableaux for Modal Logics Computational Properties, Complexity and Methodology
- Computer Science
- 2000
The paper presents a number of the computational results about SST (confluence, decidability, space complexity, modularity, etc.) and compares SST with other formalisms such as translation methods, modal resolution, and Gentzen-type tableaux and presents the methodology underlying the construction of the correctness and completeness proofs.
Single Step Tableaux for Modal
- Computer Science
- 1998
The paper presents a number of the computational results about SST (connu-ence, decidability, space complexity, query combination etc.) and compares SST with other formalisms such as translation methods, modal resolution and Gentzen-type tableaux and discusses the feasibility and unfeasibility of deriving decision procedures for SST.
Single Step Tableaux for Modal Logics
- MathematicsJournal of Automated Reasoning
- 2004
The paper presents a number of the computational results about SST (confluence, decidability, space complexity, modularity, etc.) and compares SST with other formalisms such as translation methods, modal resolution, and Gentzen-type tableaux and the methodology underlying the construction of the correctness and completeness proofs is presented.
Modal Logics with Weak Forms of Recursion: PSPACE Specimens
- Computer ScienceAdvances in Modal Logic
- 2000
It is shown that every right linear grammar logic has a satisfiability problem in deterministic exponential time and there are countably infinite classes of rightlinear grammar logics that contain weak forms of recursion that can be solved in polynomial space.
Complexity of Simple Dependent Bimodal Logics
- MathematicsTABLEAUX
- 2000
It is proved that K ⊕ ⊆ S5 is EXPTIME-hard and it is shown that for \(\langle L_1, L_2 \rangle \in K,T,B,S4 \times S4,S5\), \({\cal L}_1 \oplus_{\subseteq} {\cal L]_2\) is also EXPTime-hard.
Termination of Derivations in a Fragment of Transitive Distributed Knowledge Logic
- Computer ScienceInformatica
- 2008
By relying on the constructed loop-check-free sequent calculus a PSPACE procedure to determine a termination of backward derivation in considered fragment of the logic S4 nD is presented.
An O ((n·log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic
- Computer ScienceFTP
- 1998
A simple embedding of Grz into decidable fragments of classical first-order logic such as FO2 and the guarded fragment is presented, which uses the syntactic relationships between cut-free sequent-style calculi for Grz, S4 and T.
The Nondeterministic Information Logic NIL is PSPACE-complete
- Computer ScienceFundam. Informaticae
- 2000
It is shown to be an easy consequence of PSPACE-hardness of the well-known modal logic S4, and the main difficulty is to show that NIL satisfiability is in PSPACE.
Hintikka Multiplicities in Matrix Decision Methods for Some Propositional Modal Logics
- MathematicsTABLEAUX
- 1997
This work is a study of the inter-translatability of two closely related proof methods, i.e. tableau (or sequent) and connection based, in the case of the propositional modal logics K, K4, T, S4,…
Advances in Modal Logic, Volume 4
- Philosophy, Computer Science
- 2001
By working in a hybrid logic setting, this work is able to develop a model-theoretic understanding of both assertional and terminological information in description logic, and shows how to use the connection between description and hybrid logics to transfer results on complexity and expressive power from one to the other.
References
SHOWING 1-10 OF 16 REFERENCES
Propositional Abduction in Modal Logic
- PhilosophyLog. J. IGPL
- 1995
The similarities and diierences between quantiiers and modal operators are investigated and proof theoretical abduction methods for the modal systems K, D, T and S4 are deened, that are sound and complete.
Uniform and Non Uniform Strategies for Tableaux Calculi for Modal Logics
- MathematicsJ. Appl. Non Class. Logics
- 1995
The definition of complete strategies in tableaux calculi for propositional modal logics using a non exhaustive backtracking mechanism, a selective periodicity test and a uniform or a non uniform priority on the order of application of the tableaux rules is defined.
The Computational Complexity of Provability in Systems of Modal Propositional Logic
- Computer Science, MathematicsSIAM J. Comput.
- 1977
The computational complexity of the provability problem in systems of modal propositional logic is investigated. Every problem computable in polynomial space is $\log $ space reducible to the…
A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief
- PhilosophyArtif. Intell.
- 1992
Modal Theorem Proving
- Philosophy, MathematicsCADE
- 1986
The first-order resolution rule for classical logic is modified to handle quantifiers directly and this new resolution rule enables us to extend the authors' propositional systems to complete first- order systems.
Proof Methods for Modal and Intuitionistic Logics
- Philosophy
- 1983
One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.-…
Gentzen-type systems and resolution rules. Part I. Propositional logic
- PhilosophyConference on Computer Logic
- 1988
On a contractionfree sequent calculus for the modal logic S 4
- Arti cial Intelligence
- 1992
Resolution modal logic
- Logique et Analyse,
- 1985