By Heinrich Wansing (auth.)

This monograph offers a logical remedy of 2 principal points of the concept that of data, particularly info processing and knowledge constitution. The constitution of knowledge is handled as an issue in version thought, whereas details processing is visible as a side of facts concept. a large spectrum of substructural subsystems of intuitionistic propositional good judgment and of Nelson's positive good judgment with powerful negation is investigated. particularly, the issues of cut-elimination, useful completeness, and coding of proofs with lambda-terms are dealt with. ultimately, an interpretation of those structures by way of states of knowledge and operations over those states is presented.

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5 Model fragment classes 25 specific device, and a model fragment is the specific set of equations describing some physical phenomenon in a specific component. , descriptions of classes of components and model fragments t h a t can be instantiated to create structural descriptions and models for a variety of devices. To this end, we have devised an implemented language for specifying class level descriptions of components and model fragments. We now describe this language, and show how we represent the information described above.

1. Let E be a set of independent equations, and let F1 : E ---* P ( E ) and F2 : E ~ P ( E ) be onto causal mappings. Then tc(CF1) = tc(Cr2). Proof. To show that tc(CF1) = tC(CF~) we need to show that tc(CF1) C_ tc(Cr2) and tc(CF2) C tc(CFI). We prove the first containment, with the second containment following by a symmetric argument. To show that tc(CF1 ) C tc(CF2), it suffices to show that CF, C_ tc(Cr2), since tc(tc(CF~)) = lc(CF~). Let (q,p) E Crl, and let e G E such that Fl(e) = p, and hence q E P(e).

For example, if r e s i s t a n c e ( w i r e - l ) = r e s i s t a n c e - p a r a m e t e r - I , then evaluating the term ( r e s i s t a n c e ? o b j e c t ) for the instance w i r e - 1 results in r e s i s t a n c e - p a x a m e t e r - 1 Hence, if w i r e - 1 is modeled as a R e s i s t o r , then w i r e - 1 inherits the equation: (= voltage-parameter-I (* resistance-parameter-i current -parameter- I ) ) A s s u m p t i o n classes. The assumption-class clause in a model fragment class specifies the assumption class of the model fragments which are instances of the model fragment class.