Aggregated fuzzy answer set programming

Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics

Extending boolean regulatory network models with answer set programming

Because of their simplicity, boolean networks are a popular formalism to model gene regulatory networks. However, they have their limitations, including their inability to formally and unambiguously define network behaviour, and their lack of the possibility to model meta interactions, i.e., interactions that target other interactions. In this paper we develop an answer set programming (ASP) framework that supports threshold boolean network semantics and extends it with the capability to model meta interactions. The framework is easy to use but sufficiently flexible to express intricate interactions that go beyond threshold network semantics as we illustrate with an example of a Mammalian cell cycle network. Moreover, readily available answer set solvers can be used to find the steady states of the network

Communicating answer set programs

Answer set programming i s a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules

Towards possibilistic fuzzy answer set programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers

Foundations of fuzzy answer set programming

Answer set programming (ASP) is a declarative language that is tailored towards combinatorial search problems. Although ASP has been applied to many problems, such as planning, configuration and verification of software, and database repair, it is less suitable for describing continuous problems. In this thesis we therefore studied fuzzy answer set programming (FASP). FASP is a language that combines ASP with ideas from fuzzy logic -- a class of many-valued logics that are able to describe continuous problems. We study the following topics: 1. An important issue when modeling continuous optimization problems is how to cope with overconstrained problems. In many cases we can opt to allow imperfect solutions, i.e. solutions that do not satisfy all constraints, but are sufficiently acceptable. However, the question which one of these imperfect solutions is most suitable then arises. Current approaches to fuzzy answer set programming solve this problem by attaching weights to the rules of the program. However, it is often not clear how these weights should be chosen and moreover weights do not allow to order different solutions. We improve upon this technique by using aggregators, which eliminate the aforementioned problems. This allows a richer modeling language and bridges the gap between FASP and other techniques such as valued constraint satisfaction problems. 2. The wishes of users and implementers of a programming language are often in direct conflict with each other. Users prefer a rich language that is easy to model in, whereas implementers prefer a small language that is easy to implement. We reconcile these differences by identifying a core language for FASP, called core FASP (CFASP), that only consists of non-constraint rules with monotonically increasing functions and negators in the body. We show that CFASP is capable of simulating constraint rules, monotonically decreasing functions, aggregators, S-implicators and classical negation. Moreover we remark that the simulations of constraints and classical negation bear a great resemblance to their simulations in classical ASP, which provides further insight into the relationship between ASP and FASP. 3. As a first step towards the creation of an implementation method for FASP we research whether it is possible to translate a FASP program to a fuzzy SAT problem. We introduce the concept of the completion of a FASP program and show that for programs without loops the models of the completion coincide with the answer sets. Furthermore we show that if a program has loops, we can translate the program to a fuzzy SAT problem by generalizing the concept of loop formulas. We illustrate this on a continuous version of the k-center problem. Such a translation is important because it allows us to solve FASP programs by means of solvers for fuzzy SAT. Under the appropriate conditions it is for example possible to solve FASP programs by means of off-the-shelf solvers for mixed integer programming (MIP)

Visualization of argumentation as shared activity

The use of argumentation maps in CSCL does not always provide students with the intended support for their collaboration. In this chapter we compare two argumentation maps from two research projects, both meant to support the collaborative writing of argumentative essays based on external sources. In the COSAR-project, the Diagram-tool with which students could specify positions, proarguments, con-arguments, supports, refutations and conclusions in a free graphical format to write a social studies essay, was highly appreciated by students and teachers, but did not result in better essays. In the CRoCiCL-project, the Debate-tool with which students could specify positions, proarguments, con-arguments, supports and refutations in a structured graphical format, meant to visualize the argumentative strength of the positions, resulted in better history essays. The difference in representational guidance between both tools might explain these differences in effects, with the Debate-tool stimulating students to attend to the justification of positions and their strengths

Quality of group interaction, ethnic group composition, and individual mathematical learning gains

High-quality helping behavior is essential for effective peer interaction and learning. This study focused on ethnic group composition and the quality of group interaction as predictors of individual mathematics performance. Video-observations of 92 fifth-grade students working in groups balanced on mathematics performance level were analyzed. We expected a difference in the quality of interaction and test scores of native and non-native students. Multilevel analysis identified process regulation and giving answers as positive predictors of mathematics performance, whereas giving or applying explanations contributed negatively. Non-native students generally had lower achievement scores than native students. Non-native students working in ethnically heterogeneous groups performed better than did students working in homogenous groups. Homogeneous groups used more high-quality helping behaviors and engaged more often in task-oriented behavior. Heterogeneous groups engaged more often in low-quality helping behaviors. Working with native students may have been conducive to non-native students’ understanding of word problems in realistic mathematics education

A core language for fuzzy answer set programming

A number of different Fuzzy Answer Set Programming (FASP) formalisms have been proposed in the last years, which all differ in the language extensions they support. In this paperwe investigate the expressivity of these frameworks. Specificallywe showhowa variety of constructs in these languages can be implemented using a considerably simpler core language. These simulations are important as a compact and simple language is easier to implement and to reason about, while an expressive language offers more options when modeling problems