BringsItAboutThat\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{Brings~It~About~That}$$\\end{document} Operators Decomposed with Relating Semantics

Abstract

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic bringing it about that. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules.