In general, chemical problems are composed by complex systems. There are several chemi‐ cal processes that can be described by different mathematical functions (linear, quadratic, exponential, hyperbolic, logarithmic functions, etc.). There are also thousands of calculated and experimental descriptors/molecular properties that are able to describe the chemical be‐ havior of substances. In sever...

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...

A formal consideration in this paper is given for the essential notations to characterize the object that is distinguished in a problem domain. The distinct object is represented by another idealized object, which is a schematic element. When the existence of an element is significant, then a class of these partial elements is dropped down into actual, potential and virtual objects. The potenti...

B Proofs 3 B.1 Well-Formed Types and Environments . . . . . . . 3 B.2 Subtyping Inversion Lemma . . . . . . . . . . . . 3 B.3 Store Typing . . . . . . . . . . . . . . . . . . . . . 4 B.4 Values Inversion Lemma . . . . . . . . . . . . . . 6 B.5 Substitution . . . . . . . . . . . . . . . . . . . . . 9 B.6 Free Variables Lemma . . . . . . . . . . . . . . . 12 B.7 Well-Form Lemmas . . . . . . . . ....

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization ...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...