Спор об объеме логики в Германии первой половины XIX в.: дисциплинарные границы логического знания
The following paper considers the debate on disciplinary boundaries of logic in German philosophy of the early 19th century. It is supposed to distinguish four competing views on understanding of the logical knowledge. The analysis of the controversy enables to adjust the location of the Hegelian idea of the "Science of Logic," project and to clarify the historical context of the emergence of formal logic as a discipline.
The textbook contains the basic information of formal logical systems. It is Boolean functions, Post’s theorem on functional completeness, the k-valued logic, derivatives of Boolean functions, axiomatic calculi for propositions, for predicates, for sequentions, for resolutions. Programming language Prolog and axiomatic programming language OBJ3 are introduced. Problems of monadic logic, of finite automata and of the represented by them languages, of temporal logic are considered. Many examples are shown. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty of National research university Higher school of economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.
9th International Joint Conference, IJCAR 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 14-17, 2018, Proceedings
This text is concerned with the problem of the reciprocity between logic and human reasoning. This problem is illustrated with implementation of the theory of Wilhelm Wundt and a concrete investigation of the reasoning of people with autism and attention deficit hyperactivity disorder (ADHD) undertaken by Keith Stenning and Michiel van Lambalgen as case studies. On the one hand, the analysis of these cases reveals which of Wundt’s ideas are currently important for philosophy of logic and psychology. On the other hand, it shows the difference between the classical psychologism and the neopsychologism.
We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle's system appears then as a fragment of a broader system which can be developed by using FOL.
Logical frameworks allow the specification of deductive systems using the same logical machinery. Linear logical frameworks have been successfully used for the specification of a number of computational, logics and proof systems. Its success relies on the fact that formulas can be distinguished as linear, which behave intuitively as resources, and unbounded, which behave intuitionistically. Commutative subexponentials enhance the expressiveness of linear logic frameworks by allowing the distinction of multiple contexts. These contexts may behave as multisets of formulas or sets of formulas. Motivated by applications in distributed systems and in type-logical grammar, we propose a linear logical framework containing both commutative and non-commutative subexponentials. Non-commutative subexponentials can be used to specify contexts which behave as lists, not multisets, of formulas. In addition, motivated by our applications in type-logical grammar, where the weakenening rule is disallowed, we investigate the proof theory of formulas that can only contract, but not weaken. In fact, our contraction is non-local. We demonstrate that under some conditions such formulas may be treated as unbounded formulas, which behave intuitionistically.
Philosophy played a very specific role in the Soviet system of science and education. What happened to philosophy after the collapse of the Soviet Union? According to statistics, the number of universities in the Russian Federation that offer educational programs in the field of philosophy increased almost 10 times in the post-Soviet period: from 5 to 47. How can we explain this growth and what does it mean in terms of the dynamics of disciplines within the scope of humanities?