In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity of (...) information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results, among them: certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence. (shrink)

We are in the information age. Nowadays, the information is a high power commodity. Your domain and handling have high economic, political, social value. However, we still know little about it. What is the information? How do we store it, retrieve it and manipulate it? Everyone have or should have equal access to information? What is the relationship between information and knowledge? How can both influence and be influenced by the action? Can they are modeled? The models can contribute to (...) your understanding? Information and knowledge can consolidate or destroy friendships? What are the most efficient means to produce, store, organize and retrieve knowledge and information? Such questions permeate the content of this book, bringing together Brazilian and foreign authors, seeking to contribute to the improvement of the understanding of each of the concepts involved and the relationships between them. This work is the result of EIICA IX, International Meeting information, knowledge and action, held between December, 2nd and 4th 2015, at the Faculty of Philosophy and Science of UNESP/ Marília. (shrink)