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Jan Woleński

Abstract

The paper discusses the concept of adequacy central for Pertażycki’s methodology. According to Petrażycki any valuable scientific theory should be adequate, that is, neither limping (to broad with respect its actual scope) nor jumping (too narrow with respect to its actual scope). Consequently, adequacy of a theory is a stronger condition than its truth. Every adequacy theory is true, but not conversely. However, there is problem, because scientific laws are conditionals (implications). This suggests that adequacy is too strong conditions, because the consequence of an implication has a wider scope than its antecedent. Thus, laws should have the form of equivalence. The paper shows how model-theoretic characterization of theories allows to recognize truth and adequacy, consistently with Petrażycki’s claims.

Open access

Elena Lisanyuk and Evelina Barbashina

Abstract

In this paper we discuss L. Petrażycki’s idea of norm as a normative relation and show its repercussions in two perspectives connected to each other, in the legal theory in the framework of which it was originally introduced and where its role was straightforward, and in logic where it played a shadowy role of a fresh idea which in his expectation would have been the core of the novel logical theories capable of modelling reasoning in law and morals. We pay attention to the scholarly environment in which Petrażycki has proposed those ideas and to the unlucky fate of his academic legacy which is now being rediscovered.

Open access

Andrzej Waleszczyński, Michał Obidziński and Julia Rejewska

Abstract

The characteristic asymmetry in the attribution of intentionality in causing side effects, known as the Knobe effect, is considered to be a stable model of human cognition. This article looks at whether the way of thinking and analysing one scenario may affect the other and whether the mutual relationship between the ways in which both scenarios are analysed may affect the stability of the Knobe effect. The theoretical analyses and empirical studies performed are based on a distinction between moral and non-moral normativity possibly affecting the judgments passed in both scenarios. Therefore, an essential role in judgments about the intentionality of causing a side effect could be played by normative competences responsible for distinguishing between normative orders.

Open access

Adrian Mróz

Abstract

he process of decision making is predictable and irrational according to Daniel Ariely and other economic behaviorists, historians, and philosophers such as Daniel Kahneman or Yuval Noah Harari. Decisions made anteriorly can be, but don’t have to be, present in the actions of a person. Stories and shared belief in myths, especially those that arise from a system of human norms and values and are based on a belief in a “supernatural” order (religion) are important. Because of this, mass cooperation amongst strangers is possible.

Open access

Andrew Schumann

Abstract

In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases (e.g. on a database containing a contradiction) is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving (TIPS) by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet philosophers as an alternative to mathematical logic. The main assumption of content-genetic is that we cannot reduce our thinking to a mathematical combination of signs or to a language as such and our thought is ever cyclic and reflexive so that it contains ever a history.

Open access

Marc Besson and Barry Tesman

Abstract

In this paper, we consider T-colorings of directed graphs. In particular, we consider as a T-set the set Tr = {0, 1, 2, . . ., r−1, r+1, . . .}. Exact values and bounds of the Tr-span of directed graphs whose underlying graph is a wheel graph are presented.

Open access

Bing Wang, Jian-Liang Wu and Lin Sun

Abstract

A total-k-coloring of a graph G is a coloring of VE using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ′′(G) of G is the smallest integer k such that G has a total-k-coloring. Let G be a graph embedded in a surface of Euler characteristic ε ≥ 0. If G contains no 3-cycles adjacent to 4-cycles, that is, no 3-cycle has a common edge with a 4-cycle, then χ′′(G) ≤ max{8,Δ+1}.

Open access

Yuefang Sun, Zemin Jin and Jianhua Tu

Abstract

A total-colored graph G is rainbow total-connected if any two vertices of G are connected by a path whose edges and internal vertices have distinct colors. The rainbow total-connection number, denoted by rtc(G), of a graph G is the minimum number of colors needed to make G rainbow total-connected. In this paper, we prove that rtc(G) can be bounded by a constant 7 if the following three cases are excluded: diam() = 2, diam() = 3, contains exactly two connected components and one of them is a trivial graph. An example is given to show that this bound is best possible. We also study Erdős-Gallai type problem for the rainbow total-connection number, and compute the lower bounds and precise values for the function f(n, k), where f(n, k) is the minimum value satisfying the following property: if |E(G)| ≥ f(n, k), then rtc(G) ≤ k.

Open access

Gary Chartrand, Stephen Devereaux, Teresa W. Haynes, Stephen T. Hedetniemi and Ping Zhang

Abstract

Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of GR. We introduce and study the rainbow disconnection number rd(G) of G, which is defined as the minimum number of colors required of a rainbow disconnection coloring of G. It is shown that the rainbow disconnection number of a nontrivial connected graph G equals the maximum rainbow disconnection number among the blocks of G. It is also shown that for a nontrivial connected graph G of order n, rd(G) = n−1 if and only if G contains at least two vertices of degree n − 1. The rainbow disconnection numbers of all grids Pm _ Pn are determined. Furthermore, it is shown for integers k and n with 1 ≤ kn − 1 that the minimum size of a connected graph of order n having rainbow disconnection number k is n + k − 2. Other results and a conjecture are also presented.

Open access

Boštjan Brešar, Tatiana Romina Hartinger, Tim Kos and Martin Milanič

Abstract

Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. We extend a result of Lu and Hou from [Total domination in the Cartesian product of a graph and K 2 or Cn, Util. Math. 83 (2010) 313–322] by characterizing the pairs of graphs G and H for which γt(GH)=12γt(G)γt(H) , whenever γt(H) = 2. In addition, we present an infinite family of graphs Gn with γt(Gn) = 2n, which asymptotically approximate equality in γt(GnHn)12γt(Gn)2.