We investigate the expressive power of various extensions of rst-order, inductive, and innnitary logic with counting quantiiers. We consider in particular a LOGSPACE extension of rst-order logic, and a PTIME extension of xpoint logic with counters. Counting is a fundamental tool of algorithms. It is essential in the case of unordered structures. Our aim is to understand the expressive power gai...

Marijuana is the illicit drug most commonly used worldwide. The mechanisms by which this drug affects the brain have been studied exhaustively during the last 40 years, and better understood in the last decade. For example, the discovery of receptors to which marijuana binds, has been a major achievement in neurosciences and in the study of drug addiction. Moreover, the description of the endog...

Increasingly organizations are using process mining to understand the way that operational processes are executed. Process mining can be used to systematically drive innovation in a digitalized world. Next to the automated discovery of the real underlying process, there are process-mining techniques to analyze bottlenecks, to uncover hidden inefficiencies, to check compliance, to explain deviat...

Term-generic logic (TGL) is a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. TGL has a complete Gentzen system generalizing that of first-order logic. A certain fragment of TGL, called Horn, possesses a much simpler Gentzen system,...

Ridge estimate has been suggested as an alternative to the maximum likelihood estimate in the presence of collinearity among the elements of unobservable values in measurement error models. This paper studies the local influence of minor perturbations on the ridge estimate in the measurement error model. The diagnostics under the perturbation of variance and explanatory variables are considered...

The standard first-order reading of modality does not bind individual variables, i.e., if x is free in F (x), then x remains free in 2F (x). Accordingly, if 2 stands for ‘provable in arithmetic,’ ∀x2F (x) states that F (n) is provable for any given value of n = 0, 1, 2, . . .; this corresponds to a de re reading of modality. The other, de dicto meaning of 2F (x), suggesting that F (x) is deriva...

This paper introduces a nested sequent system for predicate logic. The system features a structural universal quantifier and a universally closed existential rule. One nice consequence of this is that proofs of sentences cannot contain free variables. Another nice consequence is that the assumption of a non-empty domain is isolated in a single inference rule. This rule can be removed or added a...

In [3], Keisler proves that if Q1 is a nonstandard model of the complete theory Th(Q) of (Q;+;×; 0; 1) and C1 is the algebraic closure of Q1, then (C1; Q1) is elementarily equivalent to (C;Q) where C is the algebraic closure of Q. But if Q r 1 is the real closure of Q1 and Qr the real closure of Q, then it is observed in [1] that (Q r 1; Q1) ≡(Qr ;Q). Victor Harnik asked the following question:...

We investigate the problem of nding a computable witness for the exis-tential quantiier in a formula of the classical rst-order predicate logic. The A-resolution calculus based on the program derivation algorithm A of C-L. Chang, R. C-T. Lee and R.Waldinger is used for nding a deenite substitution t for an existentially bound variable y in some formula F , such that F ft=yg is provable. The ter...

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that a...