The first notion is semantic associated with sets of possible worlds, taken in a relaxed light sense, and we call it information as range. The greater one's range of options for what the real world is like, the less information one has. This setting reflects common sense ideas about information and uncertainty, but it also brings a more technical agenda of what information is good for and we will develop some epistemic logic showing this. In particular, ranges of options change as agents make observations, or engage in communication. This process of 'update' high-lights a key feature of information in logic, and also in general: information is always to be understood in connection with some dynamic process using and transforming it. We will look at epistemic dynamic logics for this purpose, which form a natural calculus of change in information ranges triggered by events of observation or communication.
The second major logical strand in information highlights another semantic feature, viz. that information tends to be about something that is relevent to us, and hence it crucially involves connections between different situations. This notion of information as correlation has been developed in situation theory, starting from a naturalist theory of meaning for agents living in information rich physical environments, and moving to a more abstract view of components of a distributed system whose parts show dependencies. The correlation paradigm brings with it a further agenda of the structure of situations [[Non-Well-Founded Sets|non well founded]] or 'circular' ways of classifying them, constraints on their joint behaviour, and channels which allow for information flow. As for dynamic processes accessing this correlational structure, one can again think of observation or measurement or discourse, even though these have not been modeled in traditional situation theory per se.
Finally there is a third major logical sense of information, oriented toward syntax, inference and computation. This may be the primary sense for students learning logic and being told that valid conclusions 'add no information' to the premises.