On inference from inconsistent premisses

The main object of this paper is to provide the logical machinery needed for a viable basis for talking of the consequences, the content, or of equivalences between inconsistent sets of premisses.With reference to its maximal consistent subsets (m.c.s.), two kinds of consequences of a propositional set S are defined. A proposition P is a weak consequence (W-consequence) of S if it is a logical consequence of at least one m.c.s. of S, and P is an inevitable consequence (I-consequence) of S if it is a logical consequence of all the m.c.s. of S. The set of W-consequences of a set S it determines (up to logical equivalence) its m.c.s. (This enables us to define a normal form for every set such that any two sets having the same W-consequences have the same normal form.) The W-consequences and I-consequences will not do to define the content of a set S. The first is too broad, may include propositions mutually inconsistent, the second is too narrow. A via media between these concepts is accordingly defined: P is a P-consequence of S, where P is some preference criterion yielding some of the m.c.s. of S as preferred to others, and P is a consequence of all of the P-preferred m.c.s. of S. The bulk of the paper is devoted to discussion of various preference criteria, and also surveys the application of this machinery in diverse contexts - for example, in connection with the processing of mutually inconsistent reports.     

A New Multiperiod Multiple Traveling Salesman Problem with Heuristic and Application to a Scheduling Problem

A new multiperiod variation of the M-traveling salesman problem is introduced. The problem arises in efficient scheduling of optimal interviews among tour brokers and vendors at conventions of the tourism and travel industry. In classical traveling salesman problem vocabulary, a salesman is a tour broker at the convention and a city is a vendor's booth. In this problem, more than one salesman may be required to visit a city, but at most one salesman per time period can visit each city. The heuristic solution method presented is polynomial and is guaranteed to produce a nonconflicting set of salesmen's tours. The results of an implementation of the method for a recent convention are also reported.     

An Empirical Estimation of the Investor Loss Function Associated with the Use of Analysts' Forecasts of Earnings

The aggregate investor loss function associated with the use of analysts' forecasts of earnings expresses the relation between loss and prediction error. Prior research suggested that the shape of this loss function should provide guidance in decision rules for investors. This study empirically estimates the investor loss function and finds an asymmetry in the relation between loss and analysts' prediction error. For overestimates of earnings, loss is a quadratic function of error; while for underestimates of earnings, loss is a linear function of error.