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The Derivations of Temporal Logic Formulas

. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics , 1( 3 ):529-536, 1990. [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics , 1( 1 ):55-65, 1990. [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics , 1( 1 ):153-164, 1990. [8] Czesław Bylinski. Partial functions. Formalized Mathematics , 1( 2 ):357-367, 1990. [9] Mariusz Giero. The axiomatization of propositional linear time temporal logic. Formalized Mathematics

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The Axiomatization of Propositional Linear Time Temporal Logic

. Temporal Logic and State Systems . Springer-Verlag, 2008. [10] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [11] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133-137, 1999. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. [13] Edmund Woronowicz. Many-argument relations. Formalized

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The Properties of Sets of Temporal Logic Subformulas

. [10] Czesław Bylinski. Partial functions. Formalized Mathematics , 1( 2 ):357-367, 1990. [11] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics , 1( 1 ):47-53, 1990. [12] Agata Darmochwał. Finite sets. Formalized Mathematics , 1( 1 ):165-167, 1990. [13] Mariusz Giero. The axiomatization of propositional linear time temporal logic. FormalizedMathematics , 19( 2 ):113-119, 2011, doi: 10.2478/v10037-011-0018-1. [14] Mariusz Giero. The derivations of temporal logic formulas

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Weak Completeness Theorem for Propositional Linear Time Temporal Logic

. Formalized Mathematics , 1( 1 ):165-167, 1990. [16] Mariusz Giero. The axiomatization of propositional linear time temporal logic. Formalized Mathematics , 19( 2 ):113-119, 2011, doi: 10.2478/v10037-011-0018-1. [17] Mariusz Giero. The derivations of temporal logic formulas. Formalized Mathematics , 20( 3 ):215-219, 2012, doi: 10.2478/v10037-012-0025-x. [18] Mariusz Giero. The properties of sets of temporal logic subformulas. Formalized Mathematics , 20( 3 ):221-226, 2012, doi: 10.2478/v10037-012-0026-9. [19

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Propositional Linear Temporal Logic with Initial Validity Semantics

1 This work was supported by the University of Bialystok grants: BST447 Formalization of temporal logics in a proof-assistant. Application to System Verification , and BST225 Database of mathematical texts checked by computer . R eferences [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics , 1( 1 ):41–46, 1990. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics , 1( 1 ):91–96, 1990. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite

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Model Checking. Part II

Model Checking. Part II

This article provides the definition of linear temporal logic (LTL) and its properties relevant to model checking based on [9]. Mizar formalization of LTL language and satisfiability is based on [2, 3].

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Model Checking. Part III

Model Checking. Part III

This text includes verification of the basic algorithm in Simple On-the-fly Automatic Verification of Linear Temporal Logic (LTL). LTL formula can be transformed to Buchi automaton, and this transforming algorithm is mainly used at Simple On-the-fly Automatic Verification. In this article, we verified the transforming algorithm itself. At first, we prepared some definitions and operations for transforming. And then, we defined the Buchi automaton and verified the transforming algorithm.

MML identifier: MODELC 3, version: 7.9.03 4.108.1028

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The Axiomatization of Propositional Logic

Mathematics , 1( 1 ):175–180, 1990. [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics , 1( 1 ): 55–65, 1990. [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics , 1( 1 ):153–164, 1990. [8] Czesław Byliński. Partial functions. Formalized Mathematics , 1( 2 ):357–367, 1990. [9] Mariusz Giero. Propositional linear temporal logic with initial validity semantics. Formalized Mathematics , 23( 4 ):379–386, 2015. doi:10.1515/forma-2015-0030. [10] Witold Pogorzelski. Dictionary of Formal

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