Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

New method for hybrid multiple attribute decision-making problems with decision maker's aspiration level

How can we account for decision maker's aspiration level in multiple attribute decision-making problems? This is a question that has recently gained much scholarly attention. This study draws on the prospect theory and the Dempster-Shafer theory to propose a method that can resolve this issue. First, the precise and interval numbers and linguistic labels are compared, and then, the decision matrix is transformed into a prospect decision matrix on the basis of decision maker's aspiration level. Second, the Dempster-Shafer theory is applied to aggregate the prospect values of all alternatives on each attribute using their prospect belief intervals. Third, the orders of alternatives are obtained for all decision methods by comparing prospect belief intervals. Final, the effectiveness and feasibility of the proposed method are demonstrated by using an illustrative example. © 1990-2011 Beijing Institute of Aerospace Information.

Decision Making as Theorem Proving

We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.

Construction of the Model of the Lambda Calculus System with Algebraic Operators

A lambda system with algebraic operators,lambda-plus system,is introduced.After giving the definitions of the system,we present a sufficient condition for formulating a model of the system. Finally,a model of such system is constructed.