GFO Part I Basic Principles
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10.2 Facts and Propositions

With relations, relators and roles, all components of facts are available, such that a more formal approach can be established. Since relations are entities connecting others, it is useful to consider collections of entities and their relators. The simplest combinations of relators and relata are facts. Facts are considered as parts of the world, as entities sui generis, for example ``John's being an instance of the universal Human'' or ``the book $B$'s localization next to the book $C$'' refer to facts. Note that the existence of facts is not uncontroversial in the philosophical literature. Approaches span from the denial of facts on the one hand, to their acknowledgement as the most primitive kind of entity on the other, cf. (2,64).

Further, facts are frequently discussed in connection with other abstract notions like propositions (cf. (38, chapter 4)), which are not covered in depth here. However, what can be said about propositions is that they make claims about the existence or non-existence of facts. Therefore, truth-values are assigned to propositions and they can be logically combined. In contrast, facts do not have a truth value.

There are additional notions that are frequently mentioned in connection with facts, for example states of affairs, which have yet to be included properly in GFO. With respect to representations of facts and propositions, we intend to study and integrate results from situation theory as initiated by Barwise and Perry (7). This study will consider notions like infons and situation types, and will comprise the integration of these notions with those mentioned herein, like propositions and facts.

Another aspect to be stressed refers to the kinds of entities which facts are about, as these are not necessarily individuals. For example, the fact ``Mary is speaking about humanity'' refers to a relator of type ``speaking'', which connects Mary with the universal humanity. On the basis of the relator and the types of the arguments, several kinds of facts can be distinguished. Here, one immediate option is to look at the appearance of individuals (e.g. none, at least one, all) and categories. Facts that contain at least one individual are called individual facts, while non-individual facts are called abstract.

Individual and abstract facts may be further classified. We outline a refined classification that pertains to individual facts and is important for the category of situations and situoids (discussed in sect. 11). The basis of this classification is the temporal interrelationships of the individual constituents of facts. An individual fact is called a presential fact if all of its individual constituents are presentials, which exist at the same time-boundary. Facts that are not presential facts can still be classified in many different sub-types based on similar temporal criteria. Another dimension for classification is to refer to a finer classification of the constituents, like facts about presentials, facts about processes, mixtures of these, and so forth. The development of a practically relevant classification remains to be completed.

As yet, facts themselves have only been considered as individuals. However, it appears reasonable to speak of factual universals. For instance, sentences in the form ``A man kisses a woman'', can be interpreted in a universal sense. Each relation $R$, gives rise to a factual universal $F(R)$, whose instances are composed of a relator of $R$ and its arguments. Altogether, every relator of $R$ has a corresponding fact instantiating $F(R)$.

Robert Hoehndorf 2006-10-18


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