be true, namely at least one (at least two) kiss(es). A plausible formulation is and 5 to be related as 2 < 5 no further entities are required to exist, there have but "2 < 5" cannot be extended to "2 < 5 twice". Furthermore, the sentence conceiving of both sentences as having the same syntactic form, namely R(a; b).
However, these sentences have radically dieren t linguistic environments. For inas stating that : : : ; 2 R. ha1; ani Admittedly, the sentences "John is kissing Mary" and "2 < 5" have suThe usual semantics of rst-order logic, i. e. the seman tics with respect to which to exist entities beyond John and Mary if "John is kissing Mary (twice)" is to the following: therefore to use a logical form that will support this implication. While for 2 stance, "John is kissing Mary" can be extended to "John is kissing Mary twice", is the set x; yi : x < yg of ordered pairs. This uniform analysis harmonizes with f6 "John is kissing Mary" is implied by "John is kissing Mary twice". We have cient supercial similarit y to warrant the same syntactic and semantic analysis.
Godel’s completeness theorem is proved, interprets any sentence : : : ; R(a1; an) ontologically basic relations such as causality and intentionality. Analogously, we comprehend what are sometimes referred to as \events". The loss of a moment elaborate an ontology of relations; thus in particular, the relation of inherence distinguish elementary situoids from situoids. We assume that every situoid is occurring in it. Situations are special types of situoids: they are situoids at a common that they are all dependent on substantoids. Relational moments are to situations diers essentially from that of Barwise [2], [3]. Barwise did not individualized property, event or process which is not a part of the essence of a between essential and inessential moments. Moments include individual qualities, moments which glue them together. Situations are constituted by using further which takes into account the courses and histories of the ontological entities is missing from his theory. and u is a universal associated with s. There is a basic predicate Sitel(x) for be dened as projections of situoids on to atomic (or very small) time intervals The origin of the notion of moment lies in the theory of \individual accidents" in this more general sense may change the essence of a thing. Moments have in or equivalently as situoids with an atomic (or very small) framing chronoid. elementary situoid, and a predicate Sit(x) for situoids in general. Our approach developed by Aristotle in his Metaphysics and Categories [1]. An accident is an time, so that they present a snap-shot view of parts of the world. Situations can A situoid is a part of the world that can be comprehended as a whole and of universals which are associated with s. ass(s; u) has the meaning: s is a situoid actions and passions, a blush, a handshake, thoughts and so on; moments thus thing. We use the term \moment" in a more general sense and do not distinguish dependent on a plurality of substantoids. framed by a chronoid and by a topoid. For every situoid s there is a nite n umber An elementary situation is composed of individual substances and the relational
upper level.
x; y; z; : : :; terms are variables or elements from U [ S [ K; r; s; t denote terms. si; r : h : : : ; v :: u, t: < s, t: s. s1; sni, logical functors _; ^; !; :; $, and the quantiers 8; 9. We use untyped variables rather illustrate the main groups of axioms by selecting some typical examples.
Time (for the universal \time"), Space (for the universal \space"). To the basic vocabulary we may add further symbols used for domain specic areas; the The syntax of the language GOL( ) is dened b y the set of all expressions The language includes an axiomatization capturing the semantics of the onassociated with the language GOL. Besides the logical axioms we have the folis summarized by a tuple = (S ,U; K). and by a set K of symbols used to denote individuals. An ontological signature tologically basic relations. We do not present the axiomatization in full here, but ontological signature is determined by a set S of symbols used to denote sets (in containing the atomic formulas and closed with respect to the application of the domain specic v ocabulary is called an ontological signature, denoted by . An particular extensional relations), by a set U of symbols used to denote universals, Furthermore, we use the following symbols: Sub (for the universal \substance"), lowing groups of axioms.
Among the atomic formulas are expressions of the following form: r = s, t 2 s,