Logical Investigations

Citation

Adamatzky, A. (2000), "Logical Investigations", Kybernetes, Vol. 29 No. 2, pp. 239-248. https://doi.org/10.1108/k.2000.29.2.239.1

This is the sixth issue of a well established series of annual contributions of Russian philosophers and logicians. The book collects papers written by eminent thinkers working at the edge on philosophical logic and logical philosophy whose achievements form the corpus potissimum of the contemporary scientific philosophy in Russia. The papers vary in the nature of the material discussed; however, the whole text exhibits uniformly high quality. The logical and philosophical diversity of the results is very impressive and all of the papers deserve to be carefully discussed. Here we mention a few of them.

The first relatively connected group of papers includes works on the modalities and logic of falsehood. In his paper on the theory of the logical modalities Yu V. Ivlev addresses the problem as to how we can characterize ontological modalities with the quasimatrix logics with four truth‐values: necessary truth, contingent truth, contingent falsehood, and necessary falsehood.

S.A. Pavlov continues the developing of his falsehood logic, namely FL4 logic with falsehood operator. In the logic the four truth values are interpreted as strong truth, strong falsity, both truth and falsity (paradox or antinomicity), and neither truth nor falsity (indifference or unknowingness) that are analogous to the four valued Belknap logic and one of the logics invented by von Wright. The author shows that the language of this FL4 logic allows up to four levels of consideration of logical systems and analysis of the language expression. The three sublogics of FL4 are defined: three‐valued logics FL3N and FL3B, and two‐valued logic FL2. Namely, it is shown that FL3N is a functional equivalent of Kleene’s three‐valued logic K₃. FL3B is related to the paraconsistent Asenjo’s and Priest’s logics, and FL2 is similar to the classical logic C1.

The second group deals with the time and re‐constructions. Thus Vasiliev’s imaginative non‐Aristotelian logic, which is the theory of syllogistic type, is partially reconstructed at the format level by T.P. Kostjuk. Namely, Lukasewicz’s syllogisms are proved to be adequate for the formal representation of Vasiliev’s logic; moreover, the fundamental Brentano‐Leibnitz and Bolzano’s syllogistics are given in Vasiliev’s syllogistic style.

The interpretation of Carroll’s puzzles in the light of the philosophical ideas of the Russian philosopher P. Floresky and the correspondence between mental processes and beliefs is presented by B.V. Birjukov.

Yet another historical finding is challenged by E.F. Karavaev. He found some kind of axiomatization of the temporal logic in one of the early works of Russian mathematician A.A Markov. The logic is based on the “atom of time” concept and “earlier than” relations.

The direction and reversibility of “time and becoming” are reviewed in A.M. Anisov’s paper. There he discusses the possibilities of reversing the “time” and the “becoming” in the sense of the order of moments.

The third group of contributions may be seen as potentially applied. In K.I. Bakhtijarov’s paper the technique of the automatic derivation of the conclusions from the references is described. Here elementary conjunctions are given as the logical vectors and conclusions are obtained via a series of arithmetical operations over the vectors. The efficiency of the technique is demonstrated in the two program codes made for Caroll’s logical games.

I.B. Mikirtumov investigates intentional characteristics of a function in Church’s logic of sense and denotation; this logic allows us to operate with the intentional objects, express their identity and criteria of synonymy.

The fourth remarkable group is shaped from the contributions that mystically should be together. The Boolean lattices with the implicational logics at nodes are derived in A.S. Karpenko’s paper when he extends the calculus of entailment to the implicational fragment of classical propositional logic.

E.A. Sidorenko discusses the so‐called two‐level semantics for the possible worlds (inspired by Kripke’s relational semantics) where the first, atomic level is the usual Kripke style world whereas the second, entailment level contains the formulas of the objective language. The model structure is the tuple of the set of the possible worlds and the set of binary relations. Every world is a tuple itself, i.e. consists of atomistic and entailment levels. A formula is considered to be semantically true if it is verified in each world where auto‐implication is verified.

V.M. Popov gives us the classification of the non‐standard paraconsistent reducibility relations. His classification embodies three basic classes:

1. a.

   (1) complete in the sense of deduction from consistent assumption;

2. b.

   (2) transitive; and

3. c.

   (3) closed under the rule of substitution.

He also formalizes two relations from different classes in the sequent calculi.

It is certainly impossible to even mention all results presented in the issue but a few of them must be listed briefly. They are works by G. Sandu and J. Hiipakka discussing semantic indeterminacy of the expressions relativized to the predicates; I.A. Gerasimova’s paper on Kant’s and Leibniz’s sources of the logical theory of norms linked with the problems of mind evolution; the generalizations of Brentano‐Leibniz’s and Lukasewicz’s syllogistics in the syllogistic without negative terms written by V.I. Markin; E.K. Vojshvillo’s discussion on the connection between apodictic syllogistics and ontological necessity; A.V. Chagrov’s ideas on the strict implications in modal logics closed to intuitionistic ones; avoidance of antinomies and psycho‐logistic semantics by A. Grzegorczyk; the proof of completeness of one bimodal system of knowledge and belief (KB4) given by M.N. Bezhanishvili using the Kripke style diagrams; nature of logical knowledge and justification of logical systems by E.D. Smirnova; phenomenological interpretation of logic by J.A. Slinin; and theory of mystical identity between the names and the named objects set up by G.V. Grinenko for the analyzing of the sacral texts and doctrines.

The book is genuinely interdisciplinary, it is metascientific in nature, and it must interest students and academics, and everybody whose curious philosophical mind is thirsty for the spring water of novel ideas.