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Paraconsistent sequential linear-time temporal logic : combining paraconsistency and sequentiality in temporal reasoning

Kamide N.

Reports on Mathematical Logic

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2017

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Vol. 52

3--44

EN

Inconsistency-tolerant temporal reasoning with sequential (i.e., ordered or hierarchical) information is gaining in- creasing importance in computer science applications. A logical system for representing such reasoning is thus required for ob- taining a theoretical basis for such applications. In this paper, we introduce a new logic called paraconsistent sequential linear-time temporal logic (PSLTL), which is an extension of the standard linear-time temporal logic (LTL). PSLTL can appropriately rep- resent inconsistency-tolerant temporal reasoning with sequential information. The cut-elimination, decidability, and completeness theorems for PSLTL are proved in this paper.

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Contradiction-Tolerant Process Algebra with Propositional Signals

Bergstra J. A., Middelburg C. A.

Fundamenta Informaticae

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2017

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Vol. 153, nr 1/2

29--55

EN

In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on classical propositional logic. In this paper, we present a version of ACPps built on a paraconsistent propositional logic which is essentially the same as CLuNs. There are many systems that would have to deal with selfcontradictory states if no special measures were taken. For a number of these systems, it is conceivable that accepting self-contradictory states and dealing with them in a way based on a paraconsistent logic is an alternative to taking special measures. The presented version of ACPps can be suited for the description and analysis of systems that deal with self-contradictory states in a way based on the above-mentioned paraconsistent logic.

3

Interpolation theorems for some variants of LTL

Kamide N.

Reports on Mathematical Logic

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2015

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Vol. 50

3--30

EN

It is known that Craig interpolation theorem does not hold for LTL. In this paper, Craig interpolation theorems are shown for some fragments and extensions of LTL. These theorems are simply proved based on an embedding-based proof method with Gentzen-type sequent calculi. Maksimova separation theorems (Maksimova principle of variable separation) are also shown for these LTL variants.

4

A Paraconsistent Linear-time Temporal Logic

Kamide N., Wansing H.

Fundamenta Informaticae

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2011

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Vol. 106, nr 1

1-23

EN

Inconsistency-tolerant reasoning and paraconsistent logic are of growing importance not only in Knowledge Representation, AI and other areas of Computer Science, but also in Philosophical Logic. In this paper, a new logic, paraconsistent linear-time temporal logic (PLTL), is obtained semantically from the linear-time temporal logic LTL by adding a paraconsistent negation. Some theorems for embedding PLTL into LTL are proved, and PLTL is shown to be decidable. A Gentzentype sequent calculus PLT! for PLTL is introduced, and the completeness and cut-elimination theorems for this calculus are proved. In addition, a display calculus äPLT! for PLTL is defined.

5

Risk evaluation supported by annotated paraconsistent logic: a study of a vehicle manufacturer

Albuquerque A. R., Kliewer J. B., Arruda Campos [de] I. P., Studziński C., Kliewer M.

Journal of Achievements in Materials and Manufacturing Engineering

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2009

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Vol. 32, nr 1

81-91

EN

Purpose: In the present communcation we present a FMEA derived survey questionnaire, designed to be nalysed by means of annotated paraconsistent logic techniques, which allows for both the detection of contradictions and inconsistencies on the part of the respondents, as well as for the continuous improvement of the adequacy of the instrument in itself, and its application to truck manufacture. Design/methodology/approach: The methodology used in this study is based in the partial adoption of elements and pre-requisites needed to apply the FMEA tool and the concepts of the Paraconsistent Logic, aiming to develop a method for risk of failure criticality evaluation to new products development. Findings: The main advantage of the novel method presented herein consists in the ability to integrate coherently the insights of many expert opinions, instead of relying on a single specialist to perform the FMEA, thus improving the accuracy and reliability of this kind of analysis. method proposed does not lead to future decision process but the future consequence of a today’s decision. The method here applied describes the results in an intelligible way and points that if the company decides to minimize the project risks doing all preventive actions, it will necessary to increase costs. That is, as more conservative is the strategic company approach bigger the resultant criticality indices from specialist’s evaluations more investment is need to mitigate the risks. Practical implications: As the method takes in account all specialists evaluations and strategic parameters directly related to the Company’s Strategic plan, it is considered a good project management tool concerning to the risk management process and decision making. the integration of different opinions and expertise areas, as well as multiple critical factors and failures modes analysis lead to more reliable statistics analysis and reduce the company dependency of only one specialist, during critical decision process moments. Originality/value: The risk evaluation method described in this work allows project managers to make decisions related to project risks in order to mitigate threatens, maximize competitiveness factors and better explore market opportunities.

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Quasi-Possibilistic Logic and its Measures of Information and Conflict

Dubois D., Konieczny S., Prade H.

Fundamenta Informaticae

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2003

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Vol. 57, nr 2-4

101--125

EN

Possibilistic logic and quasi-classical logic are two logics that were developed in artificial intelligence for coping with inconsistency in different ways, yet preserving the main features of classical logic. This paper presents a new logic, called quasi-possibilistic logic, that encompasses possibilistic logic and quasi-classical logic, and preserves the merits of both logics. Indeed, it can handle plain conflicts taking place at the same level of certainty (as in quasi-classical logic), and take advantage of the stratification of the knowledge base into certainty layers for introducing gradedness in conflict analysis (as in possibilistic logic). When querying knowledge bases, it may be of interest to evaluate the extent to which the relevant available information is precise and consistent. The paper review measures of (im)precision and inconsistency/conflict existing in possibilistic logic and quasi-classical logic, and proposes generalized measures in the unified framework.