Grzegorczyk’s Logics. Part I

AbstractThis article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]). This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced by Roman Suszko in [15]. In particular, we were inspired by Suszko’s semantics for his non-Fregean logic SCI, presented in [16].Department of Mathematics and Statistics, University of Helsinki, FinlandGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Joanna Golinska-Pilarek and Taneli Huuskonen. Logic of descriptions. A new approach to the foundations of mathematics and science. Studies in Logic, Grammar and Rhetoric, 40(27), 2012.Joanna Golinska-Pilarek and Taneli Huuskonen. Grzegorczyk’s non-Fregean logics. In Rafał Urbaniak and Gillman Payette, editors, Applications of Formal Philosophy: The Road Less Travelled, Logic, Reasoning and Argumentation. Springer, 2015.Andrzej Grzegorczyk. Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, XLVII(4), 2012. In Polish.Taneli Huuskonen. Polish notation. Formalized Mathematics, 23(3):161-176, 2015. doi:1 0.1515/forma-2015-0014.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.Roman Suszko. Non-Fregean logic and theories. Analele Universitatii Bucuresti. Acta Logica, 9:105-125, 1968.Roman Suszko. Semantics for the sentential calculus with identity. Studia Logica, 28: 77-81, 1971.Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990

Logic. of Descriptions. A New Approach to the Foundations of Mathematics and Science

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems

Closer-to-nature forest management approaches in Finland

The European Commission Biodiversity Strategy for 2030 proposes to continue and further develop biodiversity-friendly practices, such as closer-to-nature-forestry, to achieve the ambitious biodiversity targets. In Finland, forestry land covers 86% of the land area and thus the protection of biodiversity is closely connected to forest management. In this report we review the elements in Finnish forest legislation, PEFC-forest certification scheme and forest management guidelines that are related to and support closer-to-nature forest management practices. We include a brief description of the specific features of boreal forest ecosystems, forest resources of Finland as well as a brief description of the forest management practices and governance.202