Answer set programming for continuous domains: a fuzzy logic approach (Q2891285)

This book provides a lot of interesting material about fuzzy answer set programming (FASP) and some of its extensions. FASP is a domain-specific programming language tailored for optimization problems with continuous domains, e.g., the design of power networks or investment strategies. FASP is inspired by classical answer set programming (ASP), which is now a well-established language for modelling of combinatorial optimization problems. In this book, the fuzzification of ASP is done by using a theory of fuzzy operations (negations, t-norms, etc.) as well as by methods of formal fuzzy logic.NEWLINENEWLINEOriginal contributions include: A) A novel approach to FASP with an attached aggregating expression to the program. It is called AFASP (aggregated fuzzy answer set programming) and allows some rules of FASP programs to be only partially satisfied without the necessity to state weights for individual rules. In AFASP the order structure used by the aggregating expression is generally different from the underlying lattice of truth values. Various potentially useful aggregators are discussed. Possibly there is a room for the use of generalized quantifiers, too. B) A new core language for FASP called CFASP (i.e., core FASP) which is much simpler than FASP (constraints are eliminated and rule bodies can contain only negators and monotonically increasing functions) and, at the same time, it allows to simulate many constructs and extensions of FASP, including constraints, monotonically decreasing functions, AFASP, S-implicators and strong negation. C) Reduction of a class of FASP programs to fuzzy SAT. It enables to construct FASP solvers based on known techniques for solving fuzzy satisfiability problems, e.g., mixed-integer programming. FASP programs reducible to fuzzy SAT by the presented method can have only t-norms and negators in the bodies of their rules. Difficulties arising in more general situations are also discussed.NEWLINENEWLINEThe book is well written and methodologically sound. The presentation is clear, there are many interesting examples. A list of symbols would, however, be a useful thing making orientation in the text more comfortable. It is certainly valuable for anyone interested in (fuzzy) logic programming and/or applied fuzzy logic.