Modus tollens

In its simpler form, the idea of falsification can be derived from the laws of Logic in fact, if Th stands for theory and Ex for experimental result, the modus tollens gives... 

We can obtain a similar result for a modus tollens deduction as follows ... 

This Is, in fact, a modus tollens calculation which proceeds In a very similar way, but with perhaps, at first, slightly surprising results as we see in Fig. 6.17 (a).-(e). 

This formulation of the problem illustrates a feature of modus tollens deduction. In order to understand this it is perhaps easiest to look at the truth table for implication in ordinary binary logic Table 2,1. U AD B and if B is true, then A may be true 01 false but if B is false then A is false. This means that the best information one can obtain concerning the truth of B can at best only leave you undecided about the truth of A. If the truth of B is somewhere between false and true, then A will be correspondingly somewhere between false and undecided. Thus in fuzzy logic, if the truth of B is between unrestricted and absolutely true, then we will still be undecided about the truth of A. If the truth... 

Having obtained a possibility measure of the perfection of the calculation model then the truth of the statement that this possibility is high can simply be obtained by inverse truth functional modification. This is then used in the modus ponens deduction to obtain a truth of NPFR. This truth is a restriction on the fuzzy set P so a new fuzzy set P" can be obtained by truth functional modification. Another inverse truth functional modification gives us the truth that the notional probability of failure is low (i.e. v(NPF)). Finally, this is used in more modus tollens deductions to give a truth restriction upon the safety of the structure S. 

All of these logical statements are arranged in a deductive hierarchy as previously. The input truth restrictions are put upon the lowest statements such as RHD, RHP, RHE, RHC, RHI and DER, DET, DEM, DEEC, CEM, CEC, CEEC, CEEG, CLP and so on. The modus tollens deductions then lead eventually to the calculation of a truth restriction upon S. It is this truth restriction which is the measure of structural safety. It could be used, for example, in other calculations such as the comparison of alternative design solutions, outlined in Section 6.4. 

FIGURE 4.1 The application of the modus tollens form of argument to a three-taxon statement. H1.3 = Hypotheses 1-3. For further explanation see text. (After Cartmill, M., Z Zoo/. Syst EvoL, 19, 73-96, 1981.)... 

Lakatos needs a critical evaluation of theories in his system just as much as Popper, and just like Popper he did not allow ad hoc auxiliary hypotheses that are not independently testable to distort such critical evaluation of competing theories. Both Lakatos and Popper understood hypotheses in the sense of universal propositions and both employed the modus tollens form of argument. Whether the emphasis is on corroboration or falsification, this very distinction cannot be had outside Popper s solution to the logical problem of induction, for it only can provide that very asymmetry, and hence the basis on which to distinguish falsificationism from verificationism. ... 

Four of them, modus ponens (MP), modus tollens (MT), abduetion, and modus ponens with trick (MPT) are well known in AI and eomputer scienee, butthe other fourneed some elarifieation. First of all, we illustrate modus tollens with triek with an example. We may know that ... 

Therefore, we have/ Socrates is human, based on modus tollens with trick, and the knowledge in the knowledge base (KB) (note that Q Socrates is not mortal). From this example, we can see that modus tollens with trick is a kind of EBR. 

We could also have the situation where goods are not available but are offered at a specific price. This varies slightly from case (1) above in that the starting point is that the goods are not available. This could, for example, be a negotiating tactic if goods will be available within a short time. This is called modus tollens with trick and takes the form ... 

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