Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and obeying treated in the same way. The suggested approach is based on the ideas of Łukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. More precisely, a consequence relation is defined on a set of statements of forms “proposition _A_ is accepted” and “proposition _A_ is rejected”, where _A_ is (...) a proposition,—a unified consequence relation. Accordingly, the rules defining a unified consequence relation,—the unified rules, have statements as premises and as conclusions. A special attention is paid to the logics in which each proposition is either accepted or rejected. If we express this property via unified rules and add them to a unified deductive system, such a unified deductive system defines a reversible unified consequence: a statement “proposition _B_ is accepted” is derived from the statement “proposition _A_ is accepted” if and only if a statement “proposition _A_ is rejected” is derived from the statement “proposition _B_ is rejected”. (shrink)

The so-called phenomenon of collective intelligence is now a burgeoning movement, with several guises and examples in many areas. We briefly survey some relevant aspects of collective intelligence in several formats, such as social software, crowdfunding and convergence, and show that a formal version of this paradigm can also be posed to logic systems, by employing the notion of logic societies. The paradigm of logical societies has lead to a new notion of distributed semantics, the society semantics, with theoretical advances (...) in defining new forms of n-valued semantics in terms of k-valued semantics, for, and applications to flying security protocols. We summarise the main advances of society semantics, commenting on their general case, the possible-translations semantics and pointing to some conceptual points and some problems and directions still to be explored. (shrink)