A comprehensive and well-organized survey of research areas related to common sense.
Common sense is a key factor in acting in the real world. Common sense encompasses both reasoning methods and knowledge that are obvious to humans but that are quite distinct from the tools of classical mathematics.
To prepare adequate logical theories for dealing with common sense, Davis introduces the notation of first-order logic. Essential to reproducing the power of ordinary language is the use of operators on sentences. Operators on sentences that apply only to a limited class of sentences, commute with the quantifiers and the boolean operators, are referentially transparent and are closed under inference, are "extensional operators" (e.g., the temporal operator). Another class of operators on sentences is that of modal operators (possible and necessary), which obey their own set of axioms. The meaning of a modal logic is defined in terms of possible-world semantics.
Classical logic needs also to be extended with plausible reasoning: degrees of belief, default rules, inference in the face of absence of information, inference about vague quantities, analogical reasoning, induction and so forth. A crucial tool for plausible reasoning is non-monotonic logic, which allows inferences to be made provisionally and, if necessary, withdrawn at any time. Next, the domain of inference must be somehow closed, and this can be done in a number of ways: the closed-world assumption (all relations relevant to the problem are mentioned in the problem statement), circumscription (extends the closed-world assumption to non-ground formulas as well, i.e. assumes that as few objects as possible have a given property), default theory (all members of a class have all the properties characteristic of the class if it is not otherwise specified). Uncertainties can be represented with probability theory.
Common sense domains to be dealt with include: physical quantities (whose values can be ordered, that can be subdivided in partially ordered intervals, that can be assigned signs based on their derivaties, whose relations can be expressed in the form of transition networks, whose behavior can be expressed in the form of qualitative differential equations); time (whose operators can be either introduced in a world of discrete, self-contained situations and events or as part of a modal logic); space (and the related concepts of distance, containment, overlapping, boundaries); physics (according to both DeKleer's component model and Forbus' qualitative process theory); propositional attitudes (specifically the relationship between belief and knowledge); actions (planning systems); and socializing (speech acts.
Davis does not discuss how common sense is learned and whether some common sense is innate.
Davis thinks that a first-order logic can be endowed with axioms that reflect the laws of the physical world. Davis' world is made of a finite set of solid objects that move in space and do not overlap. Each object has three properties: a mass distribution, an elasticity coefficient and a friction coefficient. Davis defines an onthology which includes terms such as: quantity, distance, objects, and so forth. The theory suggests that an adequate representation of the physical needs to employ Euclides' geometry, an ontology of space-temporal properties and a set of axioms about what is going on in the world.
TM, ®, Copyright © 2016 Piero Scaruffi