Quasi-characteristic inference rules for modal logics

1997 ◽  
pp. 333-341 ◽  
Author(s):  
Vladimir V. Rybakov
Keyword(s):  
Modal Logics ◽  
Inference Rules

Modal logics preserving admissible for S4 inference rules

1995 ◽  
pp. 512-526 ◽  
Author(s):  
Vladimir V. Rybakov
Keyword(s):  
Modal Logics ◽  
Inference Rules

An explicit basis for admissible inference rules in table modal logics of width 2

2009 ◽  
Vol 48 (1) ◽  
pp. 72-86
Author(s):  
V. V. Rimatskii
Keyword(s):  
Modal Logics ◽  
Inference Rules ◽  
Admissible Inference Rules

Reasoning about Petri Nets: A Calculus Based on Resolution and Dynamic Logic

2021 ◽  
Vol 22 (2) ◽  
pp. 1-22
Author(s):  
Bruno Lopes ◽  
Cláudia Nalon ◽  
Edward Hermann Haeusler
Keyword(s):  
Normal Form ◽  
Petri Nets ◽  
Dynamic Logic ◽  
Concurrent Systems ◽  
Modal Logics ◽  
Inference Rules ◽  
Logical Language ◽  
Dynamic Logics

Petri Nets are a widely used formalism to deal with concurrent systems. Dynamic Logics (DLs) are a family of modal logics where each modality corresponds to a program. Petri-PDL is a logical language that combines these two approaches: it is a dynamic logic where programs are replaced by Petri Nets. In this work we present a clausal resolution-based calculus for Petri-PDL. Given a Petri-PDL formula, we show how to obtain its translation into a normal form to which a set of resolution-based inference rules are applied. We show that the resulting calculus is sound, complete, and terminating. Some examples of the application of the method are also given.

scholarly journals Semantical Proof of Subformula Property for the Modal Logics K 4.3, KD 4.3, and S4.3

2019 ◽  
Vol 48 (4) ◽  
Author(s):  
Daishi Yazaki
Keyword(s):  
Sequent Calculus ◽  
Modal Logics ◽  
Finite Model ◽  
Inference Rules ◽  
Sequent Calculi ◽  
Model Property ◽  
Finite Model Property ◽  
Subformula Property

The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and S4.3. The application of the inference rules is said to be acceptable, if all the formulas in the upper sequents are subformula of the formulas in lower sequent. For some modal logics, Takano analyzed the relationships between the acceptable inference rules and semantical properties by constructing models. By using these relationships, he showed Kripke completeness and subformula property. However, his method is difficult to apply to inference rules for the sequent calculi for K4.3, KD4.3, and S4.3. Lookinglosely at Takano's proof, we nd that his method can be modied to construct nite models based on the sequent calculus for K4.3, if the calculus has (cut) and all the applications of the inference rules are acceptable. Similarly, we can apply our results to the calculi for KD4.3 and S4.3. This leads not only to Kripke completeness and subformula property, but also to finite model property of these logics simultaneously.

Unification and Passive Inference Rules for Modal Logics

2000 ◽  
Vol 10 (3-4) ◽  
pp. 369-377 ◽  
Author(s):  
V. V. Rybakov ◽  
M. Terziler ◽  
C. Gencer
Keyword(s):  
Modal Logics ◽  
Inference Rules

scholarly journals Admissible Inference Rules and Semantic Property of Modal Logics

2021 ◽  
Vol 37 ◽  
pp. 104-117
Author(s):  
V.V. Rimatskiy ◽  
Keyword(s):  
Modal Logic ◽  
Inference Rule ◽  
Expressive Power ◽  
Modal Logics ◽  
Human Reasoning ◽  
Inference Rules ◽  
Semantic Property ◽  
Admissible Rule ◽  
Admissible Inference Rules ◽  
Deductive Power

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

Bases of admissible inference rules for table modal logics of depth 2

1996 ◽  
Vol 35 (5) ◽  
pp. 344-349 ◽  
Author(s):  
V. V. Rimatskii
Keyword(s):  
Modal Logics ◽  
Inference Rules ◽  
Admissible Inference Rules
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