Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modeling
نویسندگان
چکیده
As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions.
منابع مشابه
Computing Utility from Weighted Description Logic Preference Formulas
We propose a framework to compute the utility of a proposal w.r.t. a preference set in a negotiation process. In particular, we refer to preferences expressed as weighted formulas in a decidable fragment of First-order Logic. Specifically, we refer to expressive Description Logics (DL) endowed with disjunction. DLs offer expressivity advantages over propositional representations, and allow us t...
متن کاملThe Power of Auxiliary Variables for Propositional and Quantified Boolean Formulas
Using auxiliary variables to introduce definitions is a popular and powerful technique in knowledge representation which can lead to shorter and more natural encodings without long repetitions. In this paper, we formally define the notion of auxiliary variables and then examine their expressive power and discuss interesting applications. We relate the idea of reusing intermediate results withou...
متن کاملRepresenting Utility Functions via Weighted Goals
We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights...
متن کاملLower complexity bounds for lifted inference
One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation language, rather than on the level of ground, propositional instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. ...
متن کاملA Semantical Analysis of Second-Order Propositional Modal Logic
This paper is aimed as a contribution to the use of formal modal languages in Artificial Intelligence. We introduce a multi-modal version of Second-order Propositional Modal Logic (SOPML), an extension of modal logic with propositional quantification, and illustrate its usefulness as a specification language for knowledge representation as well as temporal and spatial reasoning. Then, we define...
متن کامل