Sentence examples for finite model from inspiring English sources

In fact, it turns out that even when X is as strong as the full calculus of individuals, corresponding to the theory GEM of Section 4.4, there is no purely mereological formula that says whether there are finitely or infinitely many atoms, i.e., that is true in every finite model of AX but in no infinite model (Hodges and Lewis 1968).

A finite model is not merely a scaled-down version of an infinite model.

Since (under reasonable conditions) the finite model property entails decidability, this result is particularly useful.

In other words, IPDL does not possess the finite model property.

We note that all logics mentioned in this section have the finite model property and are decidable.

We study the finite model theory of Hybrid Graph Logic.

Contradictory negation and finite models.

3. Karl Schlechta (Schlechta 1997) has proved that the restriction of these theorem to finite models is a necessary one.

Hence the recursive enumeration of all valid IFL sentences yields a recursive enumeration of first-order sentences χ true in all finite models.

In defense of Kustaanheimo's approach it must be said that the connections between infinite and finite models are usually far more complex than one expects.

By Fagin's theorem (1974), this open problem can be equivalently formulated as follows: Is IFL closed under negation over finite models?