Means-End Relations and a Measure of Efficacy

Hughes, J. Carl; Esterline, Albert; Kimiaghalam, B.

doi:10.1007/s10849-005-9008-4

Cited by 13 publications

(11 citation statements)

References 15 publications

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“…The literature is not so rich with respect to Many-Valued Dynamic Logics. J. Hughes et al introduced in [18] a propositional dynamic logic over the continuum truth (0, 1)-lattice with the standard fuzzy residues. However, from the perspective of dynamic logic, this formalism is quite restrictive, since it leaves behind both transitive closure and non deterministic choice.…”

Section: L-fuzzy Dynamic Logicmentioning

confidence: 99%

On interval dynamic logic: Introducing quasi-action lattices

Santiago

Bedregal

Madeira³

et al. 2019

Science of Computer Programming

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In this paper we discuss the incompatibility between the notions of validity and impreciseness in the context of Dynamic Logics. To achieve that we consider the Lukasiewicz action lattice and its interval counterpart, we show how some validities fail in the context of intervals. In order to capture the properties of action lattices that remain valid for intervals we propose a new structure called Quasi-action Lattices which generalizes action lattices and is able to model both: The Lukasiewicz action lattice, L, and its interval counterpart, L. The notion of graded satisfaction relation is extended to quasi-action lattices. We demonstrate that, in the case of intervals, the relation of graded satisfaction is correct (c.f. Theorem 3) with respect to the graded satisfaction relation on the Lukasiewicz action lattice. Although this theorem guarantees that satisfiability is preserved on intervals, we show that validity is not. We propose, then, to weaken the notion of validity on action lattices to designated validity on quasi-action lattices. In this context, Theorem 4 guarantees that the dynamic formulae which are valid with respect to L will be designated valid with respect to L.A classic result (e.g. [10,21]) establishes that Kleene algebras are closed under formation of matrices. Fact 1The structure M n ( L) = (M n ( L), max, , 0, 1, * ) defined above is a Kleene algebra.This justifies the adoption of M n ( L) as a well behaved computational space for LDL.Definition 3. LDL-models for a set of propositions Prop and programs Π, denoted by Mod LDL (Π, Prop), consist of tuples:where W is a finite set (of states), V : Prop × W → [0, 1] is a function, and A π ∈ M n ( L), with n standing for the cardinality of W .

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Section: L-fuzzy Dynamic Logicmentioning

confidence: 99%

On interval dynamic logic: Introducing quasi-action lattices

Santiago

Bedregal

Madeira³

et al. 2019

Science of Computer Programming

View full text Add to dashboard Cite

show abstract

“…The literature is not so rich at respect of Many-Valued Dynamic Logics. J. Hughes et al introduced in [14] a propositional dynamic logic over the continuum truth (0, 1)-lattice with the standard fuzzy residues. However, from the perspective of dynamic logic, this formalism is quite restrictive, since it lefts behind both transitive closure and non deterministic choice.…”

Section: An L-fuzzy Dynamic Logicmentioning

confidence: 99%

On Interval Dynamic Logic

Santiago

Bedregal

Madeira

et al. 2016

Lecture Notes in Computer Science

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The wide number of languages and programming paradigms, as well as the heterogeneity of 'programs' and 'executions' require new generalisations of propositional dynamic logic. The dynamisation method, introduced in [20], contributed on this direction with a systematic parametric way to construct Multi-valued Dynamic Logics able to handle systems where the uncertainty is a prime concern. The instantiation of this method with the Lukasiewicz arithmetic lattice over [0, 1], that we derive here, supports a general setting to design and to (fuzzy-) reason about systems with uncertainty degrees in their transitions. For the verification of real systems, however, there are no de facto methods to accommodate exact truth degrees or weights. Instead, the traditional approach within scientific community is to use different kinds of approximation techniques. Following this line, the current paper presents a framework where the representation values are given by means of intervals. Technically this is achieved by considering an 'interval version' of the Kleene algebra based on the [0, 1] Lukasiewicz lattice. We also discuss the 'intervalisation' of L action lattice (in the lines reported in [28]) and how this class of algebras behaves as an (interval) semantics of multi-valued dynamic logic.

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“…Many-valued dynamic logics have been proposed in AI to formalize reasoning about actions with graded goals (Liau 1999) and reasoning involving probabilistic information about the outcomes of actions (Hughes, Esterline, and Kimiaghalam 2006); they have also been suggested as a formalism for reasoning about costs of program runs (Běhounek 2008), weighted computation (Madeira, Neves, and Martins 2016) and for analysing searching games (Teheux 2014). Only a handful of results on axiomatization and decidability of many-valued dynamic logics have been established and, to the best of our knowledge, no results on computational complexity of these logics are available so far.…”

Section: Introductionmentioning

confidence: 99%

Decidability and Complexity of Some Finitely-valued Dynamic Logics

Sedlár

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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Propositional Dynamic Logic, PDL, is a well known modal logic formalizing reasoning about complex actions. We study many-valued generalizations of PDL based on relational models where satisfaction of formulas in states and accessibility between states via action execution are both seen as graded notions, evaluated in a finite Łukasiewicz chain. For each n>1, the logic PDŁn is obtained using the n-element Łukasiewicz chain, PDL being equivalent to PDŁ2. These finitely-valued dynamic logics can be applied in formalizing reasoning about actions specified by graded predicates, reasoning about costs of actions, and as a framework for certain graded description logics with transitive closure of roles. Generalizing techniques used in the case of PDL we obtain completeness and decidability results for all PDŁn. A generalization of Pratt's exponential-time algorithm for checking validity of formulas is given and EXPTIME-hardness of each PDŁn validity problem is established by embedding PDL into PDŁn.

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Means-End Relations and a Measure of Efficacy

Cited by 13 publications

References 15 publications

On interval dynamic logic: Introducing quasi-action lattices

On interval dynamic logic: Introducing quasi-action lattices

On Interval Dynamic Logic

Decidability and Complexity of Some Finitely-valued Dynamic Logics

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