The mathematical theory of communication.

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.

Luciano Floridi (2003) offers a theory of information as a strongly semantic notion, according to which information encapsulates truth, thereby making truth a necessary condition for a sentence to qualify as information. While Floridi provides an impressive development of this position, the aspects of his approach of greatest philosophical significance are its foundations rather than its formalization. He rejects the conception of information as meaningful data, which entails at least three theses – that information can be false; that tautologies are (...) information; and, that It is true that ... is non-redundant – appear to be defensible. This inquiry offers various logical, epistemic, and ordinary-language grounds to demonstrate that an account of his kind is too narrow to be true and that its adoption would hopelessly obscure crucial differences between information, misinformation, and disinformation. (shrink)