Answer set programming (ASP) is a declarative programming language that enables non-monotonic reasoning through the powerful concept of negation as failure (NAF). Fuzzy ASP extends ASP in a number of ways, basically introducing gradual truth in both knowledge representation and inference. This book describes aggregated fuzzy ASP (AFASP), a particular approach for fuzzy ASP, and mostly coincides with the PhD dissertation of one of the authors, which is freely available on the Internet [1].

The book is structured as a thesis, with both strengths and weaknesses. As for its strengths, the book is strongly self-contained (too much, perhaps, since it starts from the dawn of computers) and very rigorously written. It is also rich in examples and not too difficult to read. On the other hand, the book is not intended to give deep insight into all aspects of either classical or fuzzy ASP, but mainly focuses on a specific approach. Thus, it cannot be used as a reference book for ASP, nor can it be used to comprehend the state of the art in fuzzy ASP.

The book is divided into seven chapters and is quite slim. The first two chapters introduce ASP and fuzzy logic. Rightly, the authors highlight NAF as the key feature of ASP; however, that aspect seems to disappear from chapter 3, where fuzzy ASP is introduced. In chapter 4, the proposed AFASP is presented in detail, and some alternative approaches are also described in relation to AFASP. The next two chapters describe two different techniques for translating AFASP programs into alternative languages, which may make it easier to implement (as for core fuzzy ASP in chapter 5) or faster in inference (like fuzzy SAT in chapter 6). Chapter 7 concludes the book with a summary and some notes on future work.

The AFASP approach proposed by the authors is mainly motivated by the need to partially satisfy the rules of a fuzzy ASP program in some application contexts. This is clarified by an example of fuzzy graph coloring, where a standard application of fuzzy ASP is unable to find a satisfactory coloring solution. However, this example is not well chosen, because the reader can become confused over the best way to deal with the problem. Is it better to enable partial rule satisfaction or, perhaps more simply, to restate the problem with more flexible rules that can be fully satisfied through a conventional fuzzy ASP inference? Thus, AFASP is an interesting subject to study, but its impact on concrete applications requires more convincing motivations.

Overall, the book treats a very specific topic. It is mainly intended for researchers in fuzzy ASP--those who are already knowledgeable in the general aspects of both classical and fuzzy ASP--who need the finest details on AFASP.