Formally-Verified Decision Procedures for Univariate Polynomial Computation Based on Sturm’s and Tarski’s Theorems

We study monotonic and non-monotonic Logics of Knowledge, giving decision procedures and completeness results. In particular we develop a model theory for a non-monotonic Logic of Knowledge and show that it corresponds exactly to normal applications of a non-monotonic rule of inference due to McCarthy.

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Deciding Clause Classes by Semantic Clash Resolution

Fundamenta Informaticae ◽

10.3233/fi-1993-182-406 ◽

1993 ◽

Vol 18 (2-4) ◽

pp. 163-182

Author(s):

Alexander Leitsch

Keyword(s):

Decision Procedure ◽

Decision Procedures ◽

General Concept ◽

Complexity Measure ◽

Syntactical Structure

It is investigated, how semantic clash resolution can be used to decide some classes of clause sets. Because semantic clash resolution is complete, the termination of the resolution procedure on a class Γ gives a decision procedure for Γ. Besides generalizing earlier results we investigate the relation between termination and clause complexity. For this purpose we define the general concept of atom complexity measure and show some general results about termination in terms of such measures. Moreover, rather than using fixed resolution refinements we define an algorithmic generator for decision procedures, which constructs appropriate semantic refinements out of the syntactical structure of the clause sets. This method is applied to the Bernays – Schönfinkel class, where it gives an efficient (resolution) decision procedure.

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Are there similarities between the Corona and the climate crisis?

Journal of Environmental Studies and Sciences ◽

10.1007/s13412-021-00666-5 ◽

2021 ◽

Author(s):

Robert C. Schmidt

Keyword(s):

Climate Change ◽

Political Parties ◽

Decision Procedures ◽

Free Rider ◽

Decision Makers ◽

Short Paper ◽

Political Decision ◽

Look Back ◽

Policy Measures ◽

Climate Crisis

AbstractIn this short paper, I look back at the early stages of the Corona crisis, around early February 2020, and compare the situation with the climate crisis. Although these two problems unfold on a completely different timescale (weeks in the case of Corona, decades in the case of climate change), I find some rather striking similarities between these two problems, related with issues such as uncertainty, free-rider incentives, and disincentives of politicians to adequately address the respective issue with early, farsighted and possibly harsh policy measures. I then argue that for complex problems with certain characteristics, it may be necessary to establish novel political decision procedures that sidestep the normal, day-to-day political proceedings. These would be procedures that actively involve experts, and lower the involvement of political parties as far as possible to minimize the decision-makers’ disincentives.

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Differential resolvents of minimal order and weight

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120440235x ◽

2004 ◽

Vol 2004 (54) ◽

pp. 2867-2893

Author(s):

John Michael Nahay

Keyword(s):

Upper Bound ◽

Minimal Order ◽

Determinantal Formula ◽

Differential Field ◽

Nonzero Coefficient ◽

Univariate Polynomial ◽

Linear Differential ◽

Indicial Equation

We will determine the number of powers ofαthat appear with nonzero coefficient in anα-power linear differential resolvent of smallest possible order of a univariate polynomialP(t)whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of anα-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockleα-resolvent of a trinomial and finish with a related determinantal formula.

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