Cut-free sequent and tableau systems for propositional Diodorean modal logics

  title={Cut-free sequent and tableau systems for propositional Diodorean modal logics},
  author={Rajeev Gor{\'e}},
  journal={Studia Logica},
  • R. Goré
  • Published 1 September 1994
  • Mathematics
  • Studia Logica
We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality □ is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of… 
Cut-free tableau calculi for some propositional normal modal logics
It is proved with the tableau-method that G0 is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G0is decidable and also characterisedBy the classof all frames for G0.
Strongly Analytic Tableaux for Normal Modal Logics
A strong analytic tableau calculus is presentend for the most common normal modal logics, which combines the advantages of both sequent-like tableaux and prefixed tableaux, and satisfies the strong Church Rosser property and can be fully parallelized.
Sequent Systems for Modal Logics
This chapter surveys the application of various kinds of sequent systems to modal and temporal logic, also called tense logic, using ordinary Gentzen sequents as a starting point.
A Simple Tableau System for the Logic of Elsewhere
  • S. Demri
  • Mathematics, Computer Science
  • 1996
A new proof of the NP-completeness of the satisfiability problem is given and it is shown that this problem becomes linear-time when the number of propositional variables is bounded.
On the Relational Translation Method for Propositional Modal Logics
This paper demonstrates the practical feasibility of the (relational) translation method, using a state-of-the-art theorem prover for firstorder predicate logic, and proved many benchmark theorems available from the modal logic literature.
Correspondence between Modal Hilbert Axioms and Sequent Rules with an Application to S5
There is no set of sequent rules of this format which is sound and cut-free complete for S5 and for which cut elimination can be shown by the standard permutation-of-rules argument.
Tableau Methods for Modal and Temporal Logics
This chapter gives a systematic and unified introduction to tableau methods for automating deduction in modal and temporal logics and focuses on the propositional fragments restricted to a two-valued (classical) basis.
Machine-Checked Proof-Theory for Propositional Modal Logics
We describe how we machine-checked the admissibility of the standard structural rules of weakening, contraction and cut for multiset-based sequent calculi for the unimodal logics S4, S4.3 and K4De,
Tactic-based theorem proving in first-order modal and temporal logics
A family of sequent calculi for first-order modal and temporal logics which is modular in the structure of time is introduced and a tactic-based modal/temporal theorem prover enforcing this approach is presented, obtained employing the higher-order logic programming language λ Prolog.
Bounded Proofs and Step Frames
A method is developed which detects when a specific rule-based calculus Ax axiomatizing a given logic L has the so-called bounded proof property and proves that every finite conservative one-step frame for Ax is a p-morphic image of a finite Kripke frame for L iff Ax has the boundedProof property and L hasThe finite model property.


An Algebraic Study of Diodorean Modal Systems
The present paper shows that S4.3, the extension of S4 with ALCLpLqLclqLCLqLp , is complete with respect to this interpretation when time is taken to be continuous, and that D, the extended of S 4.3 with ALNLpLCLCLCLCpLpL pLp Lp , has been identified.
A New Introduction to Modal Logic
This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
Logics of Time and Computation
Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic
Proof Methods for Modal and Intuitionistic Logics
One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.-
Temporal Logic Can Be More Expressive
Basic Modal Logic
Modal logic is meant to capture seeming entailments between such alethic and deontic notions, and a semantics for modal logic can be understood in terms of a framework of world-models.
Corrections for modal tableau calculi and interpolation by W
  • Rautenberg, JPL 12
  • 1983