scholarly journals Trie Based Subsumption and Improving the pi-Trie Algorithm

10.29007/q7h3 ◽  
2018 ◽  
Author(s):  
Andrew Matusiewicz ◽  
Neil Murray ◽  
Erik Rosenthal
Keyword(s):  
Logical Formula

An algorithm that stores the prime implicates of a logical formula in a trie was developed in [Matusiewicz et.al. 2009]. In this paper, an improved version of that pi-trie algorithm is presented. It achieves its speedup primarily by significantly decreasing subsumption testing. Preliminary experiments indicate the new algorithm to be substantially faster and the trie based subsumption tests to be considerably more efficient than the clause by clause approach originally employed.

scholarly journals Truth Degrees Theory and Approximate Reasoning in 3-Valued Propositional Pre-Rough Logic

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yingcang Ma ◽  
Juanjuan Zhang ◽  
Huan Liu
Keyword(s):  
Approximate Reasoning ◽  
Logical Formula ◽  
Concept Of Truth ◽  
Truth Degrees ◽  
Truth Degree

By means of the function induced by a logical formulaA, the concept of truth degree of the logical formulaAis introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logic is established.

scholarly journals Concession in Chinese proverbs

2019 ◽  
Vol 34 (1) ◽  
pp. 139-152
Author(s):  
Jingyao Wu
Keyword(s):  
Logical Formula ◽  
Syntactic Structures ◽  
Points Of View ◽  
Syntactic Constraints

This article studies concession in Chinese proverbs from three different points of view: syntactic, semantic and pragmatic. It is based on several previous works that focus on concession and proverbs both in French and in Chinese. To our knowledge, no research has been done on the concession in proverbs. Proverbs possess several peculiar linguistic traits that condition the expression of concession. The objective of this paper is to examine the realization of this notion under proverbial syntactic constraints as well as to highlight their logico-semantic basis and to assess their pragmatic effects. Based on our corpus of Chinese proverbs, the article not only concludes with the most common syntactic structures, universal logical formula, but also points out the argumentative force and the politeness present in concessive Chinese proverbs.

Finite Kripke models and predicate logics of provability

1990 ◽  
Vol 55 (3) ◽  
pp. 1090-1098 ◽  
Author(s):  
Sergei Artemov ◽  
Giorgie Dzhaparidze
Keyword(s):  
Modal Logic ◽  
Kripke Model ◽  
Finite Model ◽  
Kripke Models ◽  
Model Property ◽  
Logical Formula ◽  
Finite Model Property ◽  
Modal Predicate Logics ◽  
The One ◽  
Arithmetical Interpretation

AbstractThe paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic:If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that PA ⊬ fR.This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding “the predicate part” as a specific addition to the standard Solovay construction.

scholarly journals Coverage Criteria for Set-Based Specifications

2015 ◽  
Vol 22 (2) ◽  
pp. 316
Author(s):  
Maximiliano Cristiá ◽  
Joaquín Cuenca ◽  
Claudia Frydman
Keyword(s):  
Structural Testing ◽  
Test Cases ◽  
Logical Formula ◽  
Coverage Criteria ◽  
Testing Strategies ◽  
Model Based Testing ◽  
Path Coverage ◽  
Input Domain ◽  
Domain Partition ◽  
Scripting Language

Model-based testing (MBT) studies how test cases are generated from a model of the system under test (SUT). Many MBT methods rely on building an automaton from the model and then they generate test cases by covering the automaton with different path coverage criteria. However, if a model of the SUT is a logical formula over some complex mathematical theories (such as set theory) it may be more natural or intuitive to apply coverage criteria directly over the formula. On the other hand, domain partition, i.e. the partition of the input domain of model operations, is one of the main techniques in MBT. Partitioning is conducted by applying different rules or heuristics. Engineers may find it difficult to decide what, where and how these rules should be applied. In this paper we propose a set of coverage criteria based on domain partition for set-based specifications. We call them testing strategies. Testing strategies play a similar role to path- or data-based coverage criteria in structural testing. Furthermore, we show a partial order of testing strategies as is done in structural testing. We also describe an implementation of testing strategies for the Test Template Framework, which is a MBT method for the Z notation; and a scripting language that allows users to implement testing strategies.

scholarly journals Verifying Diagnosability of Discrete Event System with Logical Formula

2020 ◽  
Vol 29 (2) ◽  
pp. 304-311
Author(s):  
Xuena Geng ◽  
Dantong Ouyang ◽  
Cheng Han
Keyword(s):  
Discrete Event ◽  
Discrete Event System ◽  
Logical Formula ◽  
Event System

A theorem about infinite-valued sentential logic

1951 ◽  
Vol 16 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Robert McNaughton
Keyword(s):  
Logical Formula ◽  
Real Numbers ◽  
The Real ◽  
Truth Values ◽  
Sentential Logic ◽  
Usual Manner ◽  
Image Position

In this paper we shall use a logic with truth values ranging over all the real numbers x such that 0 ≦ x ≦ 1.1 will be “complete truth” and 0 will be “complete falsity.” The primitive sentential connectives are ‘⊃’ and ‘∼’; other connectives are ‘∨’ and ‘·’. Assume that ‘p’ and ‘q’ are sentential variables, whose truth values are respectively x and y. Then1.1. ‘p ⊃ q’ has the value min(1 − x + y, 1),1.2. ‘∼p’ has the value 1 − x,1.3. ‘p∨q’ has the value max(x, y), and1.4. ‘p·q’ has the value min (x, y).‘∨’ and ‘·’ can be defined as follows:It is the purpose of this paper to prove a theorem which will be stated in the next section. The following symbolism and convention will be used throughout the paper:S is a logical formula.ν (S) is the value of S.‘p’, ‘pi1, ’p2, …, ‘q’, are sentential variables.ν(p) = x and ν(x1) = x1, etc.ν(S) = σ and ν(S1) = σ1, etc.If S contains the sentential variables ‘p1’, ‘p2’, …, then we write for S, S(p1, P2, …). Also ν{S(p1, p2, …)) = σ(x1, x2, …).A logical formula is defined in the usual manner. 1. A sentential variable is a logical formula; 2. if S is a logical formula then ·S is a logical formula; and 3. if S and S′ are logical formulae then (S ⊃ S′) is a logical formula.

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