Language and Information
Marc Pouly, Jürg Kohlas · 2011
This chapter shows how propositional logic serves to state the truth about propositions or logical variables. It talks about systems of linear equations whose solutions provide information about the values of a set of variables. Prepositional logic or sentential calculus is concerned with the truth of elementary propositions or with the values of Boolean variables. With regard to information, the question addressed by this formalism is which propositions or variables are true and which are false. The second formalism that is considered is the systems of linear equations over sets of variables. The chapter examines the solution spaces of such systems, and introduces operations between solution spaces that are also mirrored by corresponding operations on the systems of linear equations. The final section of the chapter shows that propositional logic and linear equations over arbitrary fields are instances of a far more general generic construction called context valuation algebra. Controlled Vocabulary Terms algebra; linear differential equations