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This essay’s content is rendered by the titles of the successive sections. 1. Effective solvability versus intuitive solvability. — 2. Decidability, i.e. effective solvability, in predicate logic. The speedup phenomenon — 3. Contributions of the second-order logic to the problems of solvability — 4. The infinite progress of science in the light of Turing’s idea of the oracle. The term “oracle” is a technical counterpart of the notion of mathematical intuition.

A more detailed summary can be obtained through juxtaposing the textboxes labelled with letters A...F. Conclusion: in the progress of science an essential role is played by the feedback between intellectual intuitions (intuitive solvability) and algorithmic procedures (effective solvability).


Under some simple conditions on the real functions f and g defined on an interval I ⊂ (0, ), the two-place functions Af (x, y) = f (x) + y − f (y) and Gg(x,y)=g(x)g(y)y generalize, respectively, A and G, the classical weighted arithmetic and geometric means. In this note, basing on the invariance identity G ∘ (H, A) = G (equivalent to the Pythagorean harmony proportion), a suitable weighted extension Hf,g of the classical harmonic mean H is introduced. An open problem concerning the symmetry of Hf,g is proposed. As an application a method of effective solving of some functional equations involving means is presented.

Abductive Reasoning Driven Approach to Project - Like Production Flow Prototyping

Constraint Programming (CP) is an emergent software technology for declarative description and effective solving of large combinatorial problems especially in the area of integrated production planning. In that context, CP can be considered as an appropriate framework for development of decision making software supporting scheduling of multi-robot in a multi-product job shop. The paper deals with multi-resource problem in which more than one shared renewable and non-renewable resource type may be required by manufacturing operation and the availability of each type is time-windows limited. The problem belongs to a class of NP-complete ones. The aim of the paper is to present a knowledge based and CLP-driven approach to multi-robot task allocation providing a prompt service to a set of routine queries stated both in straight and reverse way. Provided examples illustrate both cases while taking into account an accurate as well as an uncertain specification of robots and workers operation time.


In the paper, we present our efforts to annotate evaluative language in the Prague Dependency Treebank 2.0. The project is a follow-up of the series of annotations of small plaintext corpora. It uses automatic identification of potentially evaluative nodes through mapping a Czech subjectivity lexicon to syntactically annotated data. These nodes are then manually checked by an annotator and either dismissed as standing in a non-evaluative context, or confirmed as evaluative. In the latter case, information about the polarity orientation, the source and target of evaluation is added by the annotator. The annotations unveiled several advantages and disadvantages of the chosen framework. The advantages involve more structured and easy-to-handle environment for the annotator, visibility of syntactic patterning of the evaluative state, effective solving of discontinuous structures or a new perspective on the influence of good/bad news. The disadvantages include little capability of treating cases with evaluation spread among more syntactically connected nodes at once, little capability of treating metaphorical expressions, or disregarding the effects of negation and intensification in the current scheme.