Abstract
The paper introduces an extension of the original Answer Set Prolog (ASP) by several set constructs including aggregates, defined as functions on sets. The new language, called Alog allows creating sets based on the Vicious Circle Principle by Poincaré and Russell which eliminates a number of problems found in existing extensions of ASP by aggregates. We argue that, despite the fact that Alog is not as expressive as other extensions of ASP by aggregates, clarity of its syntax and semantics, addition of several new set-based constructs, and simplicity and the ease of use make it a viable competitor to these languages. We also study a number of important properties of the language and show how ideas used in its design can be utilized to generalize and simplify the definition of another important extension of ASP by aggregates.
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