We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

We survey two basic techniques for showing that the monadic second-order theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (given for example by the restriction to formulas of a certain quantifier rank) and – depending on the fragment – reduces the model under consideration to a simpler one. In the second approach, one applies a global tran...

we consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $x$, $(x, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $x$. we also show that, for a strong residuated lattice $x$, $bigcap {p_{lambda} ,|,p_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Starting out from the assumption that monotonicity plays a central role in interpretation and inference, we derive a number of predictions about the complexity of processing quantified sentences. A quantifier may be upward entailing (i.e. license inferences from subsets to supersets) or downward entailing (i.e. license inferences from supersets to subsets). Our main predictions are the followin...

We discuss semantics of superlative quantifiers at most n and at least n. We argue that the meaning of a quantifier is a pair specifying a verification and a falsification condition for sentences with this quantifier. We further propose that the verification condition of superlative quantifiers should be interpreted in an epistemic way, that is as a conjunctive list of possibilities. We also pr...

In her dissertation, Janet Fodor has argued that the quantificational force and the intensional status of certain quantifier phrases can be evaluated independently. The proposal was only halfway accepted: the existence of non-specific transparent readings is well-established today, but specific opaque readings are deemed illusory. I argue that they are real and outline a semantic framework that...

In a previous paper, we presented an approach to calculate relational division in fuzzy databases, starting with the GEFRED model. This work centered on dealing with fuzzy attributes and fuzzy values and only the universal quantifier was taken into account since it is the inherent quantifier in classical relational division. In this paper, we present an extension of that division to relax the u...

As is well known, Buss’ theory of bounded arithmetic S 2 proves Σb0(Σ b 1) − LIND ; however, we show that Allen’s D 1 2 does not prove Σb0(Σ b 1) − LLIND unless P = NC . We also give some interesting alternative axiomatisations of S 2 . We assume familiarity with the theory of bounded arithmetic S 2 as introduced in Buss’ [2], as well as with the theory D 2 formulated by Allen in [1]. In partic...