Logical tools for handling change in agent-based systems

Abstract

The human agent in his daily activity has to deal with many situations involving change. Chief among them are the following (1) Common sense reasoning from available data. This involves predication of what unavailable data is supposed to be (nonmonotonic deduction) but it is a defeasible prediction, geared towards immediate change. This is formally known as nonmonotonic reasoning and is studied by the nonmonotonic community.(2) Belief revision, studied by a very large community. The agent is unhappy with the totality of his beliefs which he finds internally unacceptable (usually logically inconsistent but not necessarily so) and needs to change/revise it.(3) Receiving and updating his data, studied by the update community.(4) Making morally correct decisions, studied by the deontic logic community.(5) Dealing with hypothetical and counterfactual situations. This is studied by a large community of philosophers and AI researchers.(6) Considering temporal future possibilities, this is covered by modal and temporal logic.(7) Dealing with properties that persist through time in the near future and with reasoning that is constructive. This is covered by intuitionistic logic.All the above types of reasoning exist in the human mind and are used continuously and coherently every hour of the day. The formal modelling of these types is done by diverse communities which are largely distinct with no significant communication or cooperation. The formal models they use are very similar and arise from a more general theory, what we might call: "Reasoning with information bearing binary relations". Short overview of the different logicsWe will discuss the semantics of the propositional logic situation only. In all cases except the last two (i.e. Inheritance and Argumentation), the semantics consist of a set of classical models for the underlying language, with an additional structure, usually a binary relation (sometimes relative to a point of origin). This additional structure is not unique, and the result of the reasoning based on this additional structure will largely depend on the specific choice of this structure. The laws which are usually provided (as axioms or rationality postulates) are those which hold for any such additional structure. Nonmonotonic logicsNonmonotonic logics (NML) were created to deal with principled reasoning about "normal" situation. Thus, "normal" birds will (be able to) fly, but there are many exceptions, like penguins, roasted chickens, etc., and it is usually difficult to enumerate all exceptions, so they will be treated in bulk as "abnormal" birds.The standard example is -as we began to describe already -that "normal" birds will (be able to) fly, that there are exceptions, like penguins, that "normal" penguins will not fly, but that there might be exceptions to the exceptions, that some abnormal penguin might be able to fly -due to a jet pack on its back, some genetic tampering, etc. Then, if we know that some animal is a bird, call it "Tweety" as usual, and if we want to keep it as a pet, we sho...