then the value is more. In general, plausibility of conjunctions can be complicated. It may simplify somewhat for singleton C's, whence the measure would involve some kind of probability, and these phenomena would be averaged out. Having plausibility related to fraction of forced correctness is compatible with our previous definition of negative plausibilities. For disjoint hypotheses Ai and Aj, using de Morgan's theorem, the plausibility for a disjunction is similarly given, pl(Ai∨Aj) = *pl(A*i) + pl(Aj),
a bit counter-intuitively. Proceeding, thus pl(Ai → Aj) = pl(Aj) - pl(Ai).

Interestingly, this has some similarity to synaptic weight assignment in connectionist logic previously discussed where whilst some weights are increased with the addition of a clause, some are decreased. Using hardwired logic on connectionist networks, and forcing the correct values for the neurons in C, and that for a hypothesis, the final network state yields the least value for the energy function, which corresponds to the number of clauses unsatisfied. This intuitively should also represent the number of errors in C, allowing an estimation of the plausibility of the hypothesis. For this, synaptic weights, or equivalently, clauses in T need to be known explicitly; however, this can be obtained [12] through Hebbian learning. 

## Conclusions

In summary, we have explored the concept of plausibility and attempted to characterize a measure for it. In particular, we have taken an abductive basis, and conjecture that a hypothesis is more plausible if it forces more of the measured truth. For simple cases we can write down the rules for combinations. We also indicated how plausibility can be measured using a logic neural network. This exploratory proposal for plausibility needs to be further investigated, especially for the non-trivial cases of combinations. It is hoped that combination of plausibilities would help in the interpretation of combinations of measurements in experimental data.

## References

[1] L. Zadeh, "Fuzzy Sets as the Basis for a Theory of Possibility", *Fuzzy Sets and Systems* 1 (1978) 328. [2] L. A. Zadeh, "Fuzzy sets", *Information and Control* 8 (1965) 338–353. [3] G. Shafer, *A Mathematical Theory of Evidence*, Princeton Univ. Press, Princeton NJ, 1976. [4] L. Magnani, *Abduction, Reason and Science: Processes of Discovery and Explanation*, Kluwer, New York, 2001. [5] J. Ding, "Probabilistic Inferences in Bayesian Networks", *e-print arXiv:1011.0935*, 2010. [6] A Collins & R. Michalski, "The Logic of Plausible Reasoning: A Core Theory", Cognitive Science