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Vitaly I. Levin, Alexander Boldachev, Andrew Schumann, Andrzej Szelc, James Trafford, Dov M. Gabbay,

The twelfth issue:

Many-Valued Logic in the Jewish Short Stories

The Author: Vitaly I. Levin,
Jewish short stories (parables, tales, jokes, etc.) are explained from the viewpoint of many-valued logic. On the basis of some examples, we show, how their contents may be logically interpreted.

The Downward Causality and the Hard Problem of Consciousness or Why Computer Programs Do not Work in the Dark

Any low-level processes, the sequence of chemical interactions in a living cell, muscle cellular activity, processor commands or neuron interaction, is possible only if there is a downward causality, only due to uniting and controlling power of the highest level. Therefore, there is no special “hard problem of consciousness”, i.e. the problem of relation of ostensibly purely biological materiality and non-causal mentality – we have only the single philosophical problem of relation between the upward and downward causalities, the problem of interrelation between hierarchic levels of existence. It is necessary to conclude that the problem of determinacy of chemical processes by the biological ones and the problem of neuron interactions caused by consciousness are of one nature and must have one solution.

Towards New Probabilistic Assumptions in Business Intelligence

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.

Co-constructive Logics for Proofs and Refutations

The Author: James Trafford,
This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov’s logic of problems.

Interview: The Logic System is the Way You Do Logic

The Author: Dov M. Gabbay,
The interview given by Dov M. Gabbay, Augustus De Morgan Professor (Emeritus) of Logic at the Group of Logic, Language and Computation, Department of Informatics, King s College London.