# Sentence examples for first-order from high-quality English sources.

• All of them are theorems about first-order model theory.

• First order logic and second-order logic are in a sense two opposite extremes.

• Algebraic logic then broadened its interests to first order logic and modal logic.

• Nonetheless there are many results for first-order probability logic.

• Hilbert concludes his discussion of first-order logic with the remark:

• These technical results were of great importance for the subsequent debate over first-order logic.

• One reason why first order logic has such a rich model theory is that first order logic is relatively weak.

• Together, these last two points highlight just how central classical first-order logic is to Skolem's Paradox.

# Use first-order in a sentence.

• Any sentence of a first-order sentence comes with a certain quantificational depth —the number of its overlapping quantifiers.

• Independence friendly logic (IF logic, IF first-order logic) is an extension of first-order logic.

• With general models second-order logic has similar model theoretic properties as first order logic, as it can simply be thought of as many sorted first order logic (see §9.1 and Manzano 1996).

• The paper Barbosa, Martins, and Carreteiro (2014) gives an axiomatization of a fragment of first-order hybrid logic called equational first-order hybrid logic.

• First-order sentences lack the expressive power of first-order theories in general, and first-order languages lack the expressive resources of higher-order languages.

• The translations above can be extended to first-order hybrid logic, in which case the relevant target logic is two-sorted first-order logic with equality, one sort for worlds and one sort for individuals, see Chapter 6 of Braüner (2011a).

• As we will see in Section 3.6, however, not all first-order properties of temporal frames are definable by temporal formulae; and vice versa, not all properties of temporal frames that can be expressed by formulae of TL are first-order definable.

• It seems wrong that second-order evidence should always swamp the first-order verdict completely, so the calibration idea has been re-formulated so as to incorporate dependence on first-order evidence explicitly, in the evidential calibration constraint (EC):

# first-order sentence examples

• The syntax and semantics above can be extended in a number of ways, in particular, first-order machinery can be added (of course, an equivalent way to obtain first-order hybrid logic is by adding hybrid-logical machinery to first-order modal logic).

• Kripke’s 1962 “The Undecidability of Monadic Modal Quantification Theory” develops a parallel between first-order logic with one dyadic predicate and first-order monadic modal logic with just two predicate letters, to prove that this fragment of first-order modal logic is already undecidable.

• That is, there are sentences of first-order arithmetic that can be deduced from the second-order induction axiom (together with the other axioms of arithmetic, which are common to first-order and second-order arithmetic) but not from the instances of the first-order induction schema (see Shapiro 1991: 110).

• To expound them we will assume knowledge of first-order logic (see the entries on classical logic and first-order model theory) and we will call algebraic first-order languages, or simply algebraic languages, the first-order languages with equality and without any relational symbols, so that these languages have only operation symbols (also called function symbols), if any, in the set of their non-logical symbols.

first-order

## Use first-order in a sentence

On this page, there are 20 sentence examples for first-order. They are all from high-quality sources and constantly processed by lengusa's machine learning routines.