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Waste Elimination
Published in Gisi Philip, Sustaining a Culture of Process Control and Continuous Improvement, 2018
Inconsistent output can result from many factors including deviations from process standards, material shortages, excessive scrap or unexpected machine downtime. Negative trends or inconsistencies in throughput need to be investigated for root cause and addressed with appropriate countermeasures. Once a stable output is demonstrated, forecasting future results is expected to be more reliable and actionable.
An expectation operator for belief functions in the Dempster–Shafer theory*
Published in International Journal of General Systems, 2020
It has been shown (see e.g. Gilboa and Schmeidler 1994) that: If we regard as a utility function for the states of X, then Equation (6) represents a pessimistic or ambiguity-averse attitude. Also, the definition of in Equation (7) is appropriate for belief functions interpreted as credal sets of PMFs, which are not compatible with Dempster's combination rule. For a vacuous belief function on , the Choquet integral , the smallest value in . Thus, the Choquet integral is inconsistent with the central tendency semantics of probabilistic expectation.
Truth without standard models: some conceptual problems reloaded
Published in Journal of Applied Non-Classical Logics, 2018
Of course, no first-order recursively axiomatisable theory of truth for PA that allows infinitely many objects in the extension of the truth predicate is able to provide a truth predicate whose extension contains just codes of sentences in every model. However, it is reasonable to expect that the theory has at least one model (the standard one), such that the extension of the predicates is the one intended. If we adopt an -inconsistent theory of truth such as FS or PAᴌT, the interpretation of the alleged truth predicate does not seem to be appropriate in this sense. In the case of FS, due to McGee’s theorem (see the Appendix 1 for details), we know that this system entails for each and, at the same time, . Hence, by , we must have a non-standard number c in the domain satisfying . This means that there must an object in the extension of T that is the denotation of . This object must be a non-standard number as well, by the injectivity of f.
Measuring inconsistency in some branching time logics
Published in Journal of Applied Non-Classical Logics, 2021
For the first negation, ¬, we apply the standard semantics of BTLs. Recall that in our semantics, for each vertex a set of PL statements, that may be inconsistent, is asserted. But in the standard semantics, each vertex has a consistent and complete truth assignment of all the atoms. Thus, at each vertex, every PL formula is either true or false, and not both. This allows the use of logical equivalences to move negations into the PL portion of every formula. Using this approach, consider the meaning of where α is a consistent PL formula. The meaning is that it is not the case that α is true for every child of the vertex under consideration, which is equivalent to the statement that is true for some child of that vertex. Thus, is logically equivalent to ; similarly, is logically equivalent to . Next, means that it is not the case that α is true for all vertices on the branch starting at the vertex under consideration, which is equivalent to having true at some vertex on that branch. Thus, is logically equivalent to . Similarly, is logically equivalent to .