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ESSLLI 2012, Opole, Poland
The 24th meeting of the GLLI
prof. Konikowska

On 15 October 2013, Opole University hosted Professor Beata Konikowska, who holds the post of Vice Director in charge of scientific matters at the Institute of Foundations of Informatics of the Polish Academy of Sciences in Warsaw. Prof. Konikowska delivered her lecture entitled Non-deterministic Logical Matrices and their Applications.

The meeting was organized by the Institute of Mathematics and Informatics of Opole University and the Group of Logic, Language and Information (GLLI). It was held in Room 15 of Collegium Civitas of Opole University. The lecturer of the day, the invited guests and participants were welcomed by the representatives of the GLLI: Prof. Urszula Wybraniec-Skardowska and Prof. Janusz Czelakowski.

Prof. J. Czelakowski introduced the subject matter of the lecture in a general way and followed with a presentation of the scientific silhouette of the lecturer. Afterwards Prof. B. Konikowska, in her lecture, outlined the most significant ideas which lie at the foundations of non-deterministic logical matrixes (called Nmatrixes). The notion of a logical matrix is fundamental to formal semantics. Introduced by Ɓukasiewicz and Tarski in the 1930s, today it is the basic element of the greatly developed methodology of deductive systems. In the traditional framework, here referred to as deterministic one, any matrix is an ordered pair composed of an algebra similar to a propositional language and of a subset of the algebra, called the distinguished set. Nevertheless, non-deterministic matrixes allow for vagueness of algebra operations - any m-argument operation running on m-tuples of elements of the algebra allows for a possibility of choosing the value of the operation from among many options. Hence, the name - non-deterministic matrix. The idea of introducing non-deterministic logical matrixes derives from informatics, where vagueness of operations is accepted: they are thus operations of the choice type - the choice of one value out of a few or more possibilities. (The prototype here can be finite non-deterministic automata.) The element that differs non-deterministic logical matrixes from the regular ones is also the departure from the compositionalty principle that any valuation of propositional variables determines, in an unambiguous manner, the value assigned to a compound formula. In this sense valuations are not defined in a compositional way as homomorphisms of the language into the matrix algebra, as it takes place in the case of regular matrixes. Nmatrices provide adequate semantics for many logics which otherwise are not characterized by means of finite deterministic matrices. The lecturer presented certain advantages of introducing Nmatrixes, especially in the context of database managment systems.

In the discussion which followed, references were made to many intriguing items presented in the lecture.