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Partial cut elimination for propositional discrete linear time temporal logic

Jūratė Sakalauskaitė
2010 Lietuvos matematikos rinkinys  
We consider propositional discrete linear time temporal logic with future and past operators of time.  ...  For each formula ϕ of this logic, we present Gentzen-type sequent calculus Gr(ϕ) with a restricted cut rule. We sketch a proof of the soundness and the completeness of the sequent calculi presented.  ...  Rules of inference for propositional logical connectives (see Gentzen-type system G4 in [3] ).  ... 
doi:10.15388/lmr.2010.63 fatcat:cuk2cxsg5rgmrb5hugvnx4qaby

Page 5254 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
2001h:03035 a propositional temporal logic of actions. The aim of this paper is to prove the soundness and completeness of the given system.  ...  To that end we suggest and define seven different lan- guages for the propositional temporal logic of actions and illustrate the relations between these languages.” 2001h:03035 03B44 68Q60 Montanari, Angelo  ... 

Page 1224 of Mathematical Reviews Vol. , Issue 88c [page]

1988 Mathematical Reviews  
method for temporal logic based on resolution.  ...  Summary: “We present a decision method for linear temporal logic. Any given temporal formula is first converted into a normal form formula containing restricted nesting of temporal operators.  ... 

Page 4684 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
In the present paper, he establishes cut-free Gentzenizations for various propositional relevant logics with distribution, such as DJ, TJ, T and R (with different levels of contraction), and for the contractionless  ...  In particular, for the logic DW, he indicates adjustments to the Gentzenization of B and its proof; for the remaining logics, he makes adaptations to the Gentzenization and to the proof for an appropriate  ... 

Page 3152 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
This paper presents a natural deduction system for propositional tem- poral logic. Completeness and soundness are proved. The last section discusses the case of first-order temporal logic (FTL).  ...  The author considers the modal systems K, M, S4 and S5 based on a three-valued logic (true, undefined, false). First a modified Gentzen-style formalism for these systems is presented.  ... 

Page 2237 of Mathematical Reviews Vol. , Issue 88e [page]

1988 Mathematical Reviews  
The author presents a Gentzen-style sequent calculus for Reichen- bach’s three-valued propositional logic [H. Reichenbach, Philo- sophical foundations of quantum mechanics, Univ.  ...  M. de Swart on Gentzen-type formalizations for numerous modal logics, and the semantic tableau oriented work by M. Fitting.  ... 

Page 6407 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Summary: “This paper presents a deductive system for predicate temporal logic with induction.  ...  This paper presents a general structure-preserving transforma- tion scheme of cut-free Gentzen-type systems for modal predicate calculi into resolution-like systems.  ... 

Partial cut elimination for combinations of propositional multi-modal logics with past time

Jūratė Sakalauskaitė
2011 Lietuvos matematikos rinkinys  
We consider combinations of nine propositional multi-modal logics with propositional discrete linear time temporal logic with past time.  ...  For these combinations, we present sound and complete Gentzen-type sequent calculi with a restricted cut rule.  ...  Gentzen-type sequent calculi for LT , soundness Let GLTL − be a Gentzen type calculus for temporal logic LTL − introduced in Section 3.3 of [10] .  ... 
doi:10.15388/lmr.2011.ml07 fatcat:ewmpwepsxnaolmj7odkbrdflre

Page 1381 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
linear temporal logic.”  ...  Summary: “This paper presents a hybrid reasoning system similarity saturation—for first-order linear temporal logic with ‘next’ and ‘unless’.  ... 

Page 4745 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
In the present paper, the author introduces two cut-free Gentzen-style systems for the “normal formulas” of some logics without the contraction rule B, TW, EW, RW and RWK.  ...  accessibility relations, and PDL , deterministic propositional dynamic logic without Kleene-star.  ... 

Page 3134 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
The first section is devoted to a short discussion of desirable properties of Gentzen systems and a short review of various sequential systems for modal logics.  ...  {For the entire collection see MR 99k:03012.} N. C. A. da Costa (Sao Paulo) 2000e:03053 03B45 03F05 Indrzejcezak, Andrzej (PL-LODZ; Lodz) Generalised sequent calculus for propositional modal logics.  ... 

A Survey of Nonstandard Sequent Calculi

Andrzej Indrzejczak
2014 Studia Logica: An International Journal for Symbolic Logic  
modal and temporal logics. 5 General theory of labelled systems is presented in Gabbay [19]; for a survey of approaches developed for modal logics see Indrzejczak [30].  ...  The other group covers systems for modal and temporal logics, where the distinction is made inside antecedent and succedent to distinguish between formulae of different modality or temporal localization  ...  The system G * for classical propositional logic consists of axioms of the form Γ, ϕ ⇒ ϕ or Γ, ϕ, ¬ϕ ⇒ ψ and standard Gentzen (intuitionistic) rules (⇒ ∧), (∧ ⇒), (∨ ⇒) and (⇒→) with the same contexts  ... 
doi:10.1007/s11225-014-9567-y fatcat:jp5yu3ueojaarjlclhjpfdympy

Useful Four-Valued Extension of the Temporal Logic KtT4

Vincent Degauquier
2018 Bulletin of the Section of Logic  
The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds  ...  This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most  ...  Proposition 4 . 4 Let Γ ⊢ ∆ be a Gentzen sequent for L(H).Then, Γ ⊢ ∆ is H-valid if and only if τ [Γ], γ, x , τ [∆], δ, x is classic-derivable. Proposition 5. Let Γ ⊢ ∆ be a Gentzen sequent for L(B).  ... 
doi:10.18778/0138-0680.47.1.02 fatcat:acbnuqyfjrc67hmzvpf3n54qea

Page 777 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
Wallen], Tableaux for intu- itionistic logics (255-296); Rajeev Goré, Tableau methods for modal and temporal logics (297-396); Marcello D’Agostino, Dov Gabbay and Krysia Broda, Tableau methods for substructural  ...  “Tableau methods for classical propositional logic”, by D’ Agostino, is a detailed discussion of algorithms for deciding the truth of propositions, with an emphasis on the computational complexity of each  ... 

Page 5908 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
991:03003 Two-dimensional temporal logic (219-236); J. H.  ...  It is important that neither the Gentzen systems nor resolution are restricted to tree form.  ... 
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