We propose a new first-order perturbation theory that provides near-quantitative description of the thermodynamics simple fluids. The is based on ansatz Helmholtz free energy bounded below by Mayer-f expansion. Together with rigorous upper bound provided u-expansion, this brackets actual between an and (effective) lower can both be calculated theory. This great practical use. Here, two bounds a...

in this paper, a closed form solution for bending and free vibration analyses of simply supported rectangular laminated composite plates is presented. the static and free vibration behavior of symmetric and antisymmetric laminates is investigated using a refined first-order shear deformation theory. the winkler–pasternak two-parameter model is employed to express the interaction between the lam...

A new theory of evaluating counterfactual statements is presented based on the established predicate calculus formalism of the Fluent Calculus for reasoning about actions. The assertion of a counterfactual antecedent is axiomatized as the performance of a special action. An existing solution to the Ramification Problem in the Fluent Calculus, where indirect effects of actions are accounted for ...

We investigate the first-order theory of subtype constraints. We show that the first-order theory of non-structural subtyping is undecidable, and we show that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping. Our results hold for both simple and recursive types. The undecidability result is shown...

We expose a formalism that allows the expression of any theory with one or more axiom schemes using a finite number of axioms. This allows us to give finite first-order axiomatizations of arithmetic and real analysis, and a presentation of arithmetic in deduction modulo that has a finite number of rewrite rules. Overall, this formalization relies on a weak calculus of explicit substitutions to ...

We present a formalization of parts of Melvin Fitting’s book “FirstOrder Logic and Automated Theorem Proving” [1]. The formalization covers the syntax of first-order logic, its semantics, the model existence theorem, a natural deduction proof calculus together with a proof of correctness and completeness, as well as the Löwenheim-Skolem theorem.

An approximate Herbrand theorem is proved and used to establish Skolemization for first-order Łukasiewicz logic. Proof systems are then defined in the framework of hypersequents. In particular, extending a hypersequent calculus for propositional Łukasiewicz logic with usual Gentzen quantifier rules gives a calculus that is complete with respect to interpretations in safe MV-algebras, but lacks ...