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Abstract

In constructing the three-valued logic, Jan Łukasiewicz was highly inspirited by the Aristotelian idea of logical contingency. Nevertheless, we can construct a four-valued logic for explicating the Stoic idea of logical determinacy. In this system, we have the following truth values: 0 (‘possibly false), 1 (‘necessarily false’), 2 (‘possibly true’), 3 (‘necessarily true’), where the designated truth value is represented by the two values: 2 and 3.

Abstract

The logical reasoning first appeared within the Babylonian legal tradition established by the Sumerians in the law codes which were first over the world: Ur-Nammu (ca. 2047 – 2030 B.C.); Lipit-Ishtar (ca. 1900 – 1850 B.C.), and later by their successors, the Akkadians: Hammurabi (1728 – 1686 B.C.). In these codes the casuistic law formulation began first to be used: “If/when (Akkadian: šumma) this or that occurs, this or that must be done” allowed the Akkadians to build up a theory of logical connectives: “... or…”, “… and…”, “if…, then…”, “not…” that must have been applied in their jurisprudence. So, a trial decision looked like an inference by modus pones and modus tollens or by other logical rules from (i) some facts and (ii) an appropriate article in the law code represented by an ever true implication. The law code was announced by erecting a stele with the code or by engraving the code on a stone wall. It was considered a set of axioms announced for all. Then the trial decisions are regarded as claims logically inferred from the law code on the stones. The only law code of the Greeks that was excavated is the Code of Gortyn (Crete, the 5th century B.C.). It is so similar to the Babylonian codes by its law formulations; therefore, we can suppose that the Greeks developed their codes under a direct influence of the Semitic legal tradition: the code was represented as the words of the stele and the court was a logic application from these words. In this way the Greek logic was established within a Babylonian legal tradition, as well. Hence, we can conclude that, first, logic appeared in Babylonia and, second, it appeared within a unique legal tradition where all trial decisions must have been transparent, obvious, and provable. The symbolic logic appeared first not in Greece, but in Mesopotamia and this tradition was grounded in the Sumerian/Akkadian jurisprudence.

Abstract

This volume contains the papers presented at the Philosophy and History of Talmudic Logic Affiliated Workshop of Krakow Conference on History of Logic (KHL2016), held on October 27, 2016, in Krakow, Poland.

Abstract

In this paper reflexive games are defined as a way to act beyond equilibria to control our opponents by our hiding motives. The task of a reflexive game is to have the opponent’s actions become transparent for us, while our actions remain obscure for the competitor. In case a reflexive game is carried out between agents belonging to the same organisation (corporation, company, institute), success in a reflexive game can be reached by a purposeful modification of some components of a controlled system. Such a modification for the guaranteed victory in a reflexive game is called reflexive management. This kind of management uses reflexive games to control a knowledge structure of agents in a way their actions unconsciously satisfy the centre’s goals.

Abstract

It is a Preface to Volumes 7:3 and 7:4 (2018) consisting of articles presented at the International Interdisciplinary Conference Ideas and Society on the 150th anniversary of the birth of Leon Petrażycki, held on November 24, 2017, in Rzeszów, Poland.

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.

Abstract

The paper considers main features of two groups of logics for biological devices, called Physarum Chips, based on the plasmodium. Let us recall that the plasmodium is a single cell with many diploid nuclei. It propagates networks by growing pseudopodia to connect scattered nutrients (pieces of food). As a result, we deal with a kind of computing. The first group of logics for Physarum Chips formalizes the plasmodium behaviour under conditions of nutrient-poor substrate. This group can be defined as standard storage modification machines. The second group of logics for Physarum Chips covers the plasmodium computing under conditions of nutrient-rich substrate. In this case the plasmodium behaves in a massively parallel manner and propagates in all possible directions. The logics of the second group are unconventional and deal with non-well-founded data such as infinite streams.

Abstract

It is a Preface to Volume 8:2 (2019) consisting of articles presented at the International Interdisciplinary Conference anniversary of the birth of Jan Łukasiewicz, Rzeszów, Poland.

Abstract

One of the main assumptions of mathematical tools in science is represented by the idea of measurability and additivity of reality. For discovering the physical universe additive measures such as mass, force, energy, temperature, etc. are used. Economics and conventional business intelligence try to continue this empiricist tradition and in statistical and econometric tools they appeal only to the measurable aspects of reality. However, a lot of important variables of economic systems cannot be observable and additive in principle. These variables can be called symbolic values or symbolic meanings and studied within symbolic interactionism, the theory developed since George Herbert Mead and Herbert Blumer. In statistical and econometric tools of business intelligence we accept only phenomena with causal connections measured by additive measures. In the paper we show that in the social world we deal with symbolic interactions which can be studied by non-additive labels (symbolic meanings or symbolic values). For accepting the variety of such phenomena we should avoid additivity of basic labels and construct a new probabilistic method in business intelligence based on non-Archimedean probabilities.