We investigate logic programs whose rules are assigned nonnegative real numbers. These numbers are interpreted as the costs of applying rules. There are several ways in which these costs can be interpreted. In the paper, two such interpretations are discussed in detail. They are referred to as no-reusability and reusability interpretations. The former requires that an atom be paid for each time...

The existence of a model for a logic program is generally established by lattice-theoretic arguments. We present three examples to show that metric methods can often be used instead, generally in a direct, straightforward way. One example is a game program, which is not stratified or locally stratified, but which has a unique supported model whose existence is easily established using metric me...

We present a method for trust scenarios with more than one trustee, where sets of trustees are ordered in a relation of relative trustworthiness. We show how a priority structure implicit in a trust relation can be made fully explicit by means of a lattice and how a system of default expectations arises from a systematic interpretation. The default structure lends itself to formal interpretatio...

Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words. In this paper, we introduce a general model of weighted automata acting on graphs, which form a quantitative version of Thomas’ unweighted model of graph acceptors. We derive a Nivat theorem for weighted graph automata ...

Fuzzy modus ponens (briefly, FMP) is the most fundamental form of fuzzy reasoning and has been extensively discussed by diverse researchers. The aim of the present paper is to propose a formalized form of FMP, called generalized modus ponens, in the fuzzy logic system L and solve it in L, and then provide its numerical version as a new algorithm for solving FMP. As a preparation, some related q...