the problem of crack identification in continuous beam like structures is considered. the cracks’ locations and their depths are identified by employing experimental modal test results performed on the structure. the cracks are modeled using generic elements to include the coupling effects between shear forces and bending moments at the crack section. in the identification procedure eigen- sens...

Given an action theory, a goal, and a set of initial states, we consider the problem of checking whether the goal is always achievable in every initial state of the set. To address this problem, we introduce a notion of reduction between sets of states, and show that if the set of the initial states can be reduced to one of its subsets, then the problem is equivalent to checking whether the goa...

We prove that Z in definable in Q by a formula with two universal quantifiers followed by seven existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that is surjective on rational points. We also give a formula, again with universal quantifiers followed by existential quantifiers, that in any number field...

We give some characterizations of semicomputability of sets of reals by programs in certain While programming languages over a topological partial algebra of reals. We show that such sets are semicomputable if and only if they are one of the following: (i) unions of effective sequences of disjoint algebraic open intervals; (ii) unions of effective sequences of rational open intervals; (iii) uni...

In this paper, we introduce bi-approximation semantics, a two-sorted relational semantics, via the canonical extension of lattice expansions. To characterise Ghilardi and Meloni’s parallel computation, we introduce doppelgänger valuations which allow us to evaluate sequents and not only formulae. Moreover, by introducing the bi-directional approximation and bases, we track down a connection to ...

We show that, in a fairly general setting including higher-types, may, must and probabilistic testing are semidecidable. The case of must testing is perhaps surprising, as its mathematical definition involves universal quantification over the infinity of possible outcomes of a non-deterministic program. The other two involve existential quantification and integration. We also perform first step...

We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over ...

This paper argues that exhaustification is empirically and theoretically important as a tool in the semantic description of various constructions in natural language. Discussion focuses on the comparative construction, and presents a view of exhaustification as a ‘control element’ that influences the interpretation of a more basic element: the existential quantifier.

There are two main approaches to the problem of donkey anaphora (e.g. John owns a donkey. He beats it). Proponents of Discourse Representation Theory (Kamp 1981, Heim 1982) revise quantification so as to allow an existential quantifier to bind a pronoun which is not within its syntactic scope which yields a formal link between the quantifier and the pronoun, as is illustrated in (1)a. By contra...

The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by th...