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In this paper, with reference to relationships of the traditional square of opposition, we establish all the relations of the square of opposition between complex sentences built from the 16 binary and four unary propositional connectives of the classical propositional calculus (CPC). We illustrate them by means of many squares of opposition and, corresponding to them—octagons, hexagons or other geometrical objects.

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation.

Logic and linguistics have engaged in a many-faceted dialogue since the very beginnings of both disciplines in Antiquity. While participants may have had diverse views over the ages, arguably, the dialogue has always revolved around the relationship between human thought and natural language. While there are those who see these two domains as one and the same, or as a case of one-directional influence (language as an expression of thought, or thought as an expression of language), we beg to differ. To us, the long historical tradition of authors such as Arnauld, Boole, Turing, or Jespersen demonstrates the much richer perspectives on language and reasoning that are needed, including connections with intelligence and computability. Another major historical theme in the above dialogue are similarities or convergences between natural and artificial languages. It is clear that natural languages are not only semantically broader, but also much closer to human communication than artificial languages, and so linguistic grammars have long dealt with a larger set of problems than logical formalisms. Tomention just one key instance, the notion of time has always been present in grammars (whatever their normative or descriptive stance or theoretical affiliation), whereas logical frameworks either lack explicit reference to time, or treat only some selected features, falling far short of all the features of time and aspect that natural languages are capable of expressing. Even so, the goal of translating utterances to logical forms has been a never-ending source of attraction for linguists aiming for methodological rigor and metalinguistic precision. Naturally, simple conversion of utterances to some logical form does not exhaust all their

The paper enriches the conceptual apparatus of the theory of meaning and denotation that was presented in Part I (Section 3). This part concentrates on the notion of interpretation, which is defined as an equivalence class of the relation possessing the same manner of interpreting types. In this part, some relations between meaning and interpretation, as well as one between denotation an interpretational denotation are established. In the theory of meaning and interpretation, the notion of language communication has been formally introduced and some conditions of correctness of communication have been formulated.

With reference to Polish logico-philosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by object-tokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion is that in syntactic researches it is redundant to postulate the existence of abstract linguistic entities. Earlier, in a slightly different form, the idea was presented in [27] and signalled in [26] and [25].