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Axiom System

The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform

Adam Trybus – 1st expert on this subject based on the ideXlab platform

  • an Axiom System for a spatial logic with convexity
    [Thesis]. Manchester UK: The University of Manchester; 2012., 2012
    Co-Authors: Adam Trybus


    A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We Axiomatised the theory of (ROQ(R^2), conv, ?) , where ROQ(R^2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ? is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.

  • an Axiom System for a spatial logic with convexity
    European Conference on Artificial Intelligence, 2010
    Co-Authors: Adam Trybus


    This paper presents a part of work in progress on Axiomatizing a spatial logic with convexity and inclusion predicates (hereinafter called convexity logic), with some intended interpretation over the real plane. More formally, let Lconv,≤ be a language of first order logic and two non-logical primitives: conv (interpreted as a property of a set of being convex) and ≤ (interpreted as the set inclusion relation). We let variables range over regular open rational polygons in the real plane (denoted ROQ(R2)). We call the tuple M = —where primitives are defined as indicated above —a standard model. We propose an Axiomatization of the theory of M and prove soundness and completeness for this Axiomatization.

Huili Xing – 2nd expert on this subject based on the ideXlab platform

  • Refinement Modal Logic Based on Finite Approximation of Covariant-Contravariant Refinement
    IEEE Access, 2019
    Co-Authors: Huili Xing


    The notion of covariant-contravariant refinement (CC-refinement) is a generalization of the notions of bisimulation and refinement, which is coinductively defined to describe behavior relation, i.e., two related processes are required to be always able to provide matched transitions each other. The notion of CC-n-refinement, where n is a natural number, presented in this paper, finitely approximates the notion of CC-refinement through weakening the above-mentioned requirement. A process is said to CC-n-refine another process whenever they can, within n-steps, match the transitions each other, and a CC-n-refinement relation may be considered to be a CC-refinement relation if n is big enough. Based on this kind of finite approximation, this paper presents CC-n-refinement modal logic (nCCRML) obtained from the modal System K by adding CC-n-refinement quantifiers, establishes an Axiom System for nCCRML, and explores some important properties of this Axiom System: soundness, completeness, and decidability. CC-n-refinement quantifiers can be used to formalize some interesting problems in the field of formal method.

Nan Zhang – 3rd expert on this subject based on the ideXlab platform

  • verifying safety critical task scheduling Systems in pptl Axiom System
    Journal of Combinatorial Optimization, 2016
    Co-Authors: Nan Zhang, Zhenhua Duan, Mengfei Yang, Bin Gu, Cong Tian


    This paper presents a case study of formal verification of safety critical task scheduling Systems. First, a scheduling algorithm described in a temporal logic programming language is presented; then a sufficient and necessary condition for the schedulability of task set is formalized. Further, the correctness of the condition is proved by means of theorem proving in the Axiom System of Propositional Projection Temporal Logic.

  • a complete Axiom System for propositional projection temporal logic with cylinder computation model
    Theoretical Computer Science, 2016
    Co-Authors: Nan Zhang, Zhenhua Duan, Cong Tian


    To specify and verify multi-core parallel programs in a uniform framework, this paper proposes an Axiom System for CCM-PPTL which extends that of PPTL by including transformation rules for sequence expressions and Axioms as well as inference rules on the CCM construct. Further, the soundness and completeness of the extended Axiom System are proved.

  • Verification of Hardware Designs: A Case Study
    2011 First ACIS JNU International Conference on Computers Networks Systems and Industrial Engineering, 2011
    Co-Authors: Nan Zhang, Zhenhua Duan


    As size and complexity have increased, formal verification of hardware designs is a challenge to us. This paper presents a case study for verification of a full adder design using the Axiom System of Propositional Projection Temporal Logic (PPTL). The paper focuses on the functional verification of the adder. To this end, the syntax, semantics and Axiom System for PPTL are briefly introduced. Further, functions and architectures of full adders are presented respectively. Finally, the correctness of the full adder is verified.