Discriminative Gaifman Models

On the locality of arb-invariant first-order formulas with modulo counting quantifiers

We study Gaifman locality and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. This paper gives a detailed picture of locality and ...

Isomorphism Types of Trees1

Haim Gaifman Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements

There are three sections in this paper. The first is a philosophical discussion of the general problem of reasoning under limited deductive capacity. The second sketches a rigorous way of assigning probabilities to statements in pure arithmetic; motivated by the preceding discussion, it can nonetheless be read separately. The third is a philosophical discussion that highlights the shifting cont...

On the locality of arb-invariant first-order logic with modulo counting quantifiers

We study Gaifman and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. This paper gives a detailed picture of locality and non-local...

Extending Lambek Grammars to Basic Categorial Grammars

Pentus [24] proves the equivalence of LCG’s and CFG’s, and CFG’s are equivalent to BCG’s by the Gaifman theorem [1]. This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen [12], but it was deficient [4]. We use a modification of Pentus’ proof and a new proof of the Gaifman theorem on t...