Reasoning over streams of input data is an essential part of human intelligence. During the last decade {\em stream reasoning} has emerged as a research area within the AI-community with many potential applications. In fact, the increased availability of streaming data via services like Google and Facebook has raised the need for reasoning engines coping with data that changes at high rate. Recently, the rule-based formalism {\em LARS} for non-monotonic stream reasoning under the answer set semantics has been introduced. Syntactically, LARS programs are logic programs with negation incorporating operators for temporal reasoning, most notably {\em window operators} for selecting relevant time points. Unfortunately, by preselecting {\em fixed} intervals for the semantic evaluation of programs, the rigid semantics of LARS programs is not flexible enough to {\em constructively} cope with rapidly changing data dependencies. Moreover, we show that defining the answer set semantics of LARS in terms of FLP reducts leads to undesirable circular justifications similar to other ASP extensions. This paper fixes all of the aforementioned shortcomings of LARS. More precisely, we contribute to the foundations of stream reasoning by providing an operational fixed point semantics for a fully flexible variant of LARS and we show that our semantics is sound and constructive in the sense that answer sets are derivable bottom-up and free of circular justifications.

Epistemic Specifications allow for the correct representation of incomplete information in the presence of multiple belief sets by expanding Answer Set Programming with modal operators $K$ and M. The meaning of M in the existing work does not correspond well to the principle of justifiedness accepted by the community. It is, however, challenging to characterize the justfiedness of each belief, due to the complexity introduced by M. We address this issue by identifying a belief set with a program which uniquely decides the belief set. This idea leads to a novel definition of the semantics of Epistemic Specifications which assures that each belief in any belief set is well justified.  We also show that conformant planning problems can be naturally represented by Epistemic Specification under our semantics.

The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dl-programs), Hex programs, and logic programs with first-order formulas (general logic programs). However, it was recently observed that the FLP semantics may produce unintuitive answer sets with circular justifications caused by self-supporting loops. In this paper, we address the circular justification problem for general logic programs by enhancing the FLP semantics with a level mapping formalism. In particular, we extend the Gelfond-Lifschitz three step definition of the standard answer set semantics from normal logic programs to general logic programs and define for general logic programs the first FLP semantics that is free of circular justifications. We call this FLP semantics the well-justified FLP semantics. This method naturally extends to general logic programs with additional constraints like aggregates, thus providing a unifying framework for defining the well-justified FLP semantics for various types of logic programs. When this method is applied to normal logic programs with aggregates, the well-justified FLP semantics agrees with the conditional satisfaction based semantics defined by (Son, Pontelli, and Tu 2007); and when applied to dl-programs, the semantics agrees with the strongly well-supported semantics defined by (Shen 2011).

Fages [1994] introduces the notion of well-supportedness as a key requirement for the semantics of normal logic programs and characterizes the standard answer set semantics in terms of the well-supportedness condition. With the property of well-supportedness, answer sets are guaranteed to be free of circular justifications. In this paper, we extend Fages’ work to description logic programs (or DL-programs). We introduce two forms of well-supportedness for DL-programs. The first one defines weakly well-supported models that are free of circular justifications caused by positive literals in rule bodies. The second one defines strongly well-supported models that are free of circular justifications caused by either positive or negative literals. We then define two new answer set semantics for DL-programs and characterize them in terms of the weakly and strongly well-supported models, respectively. The first semantics is based on an extended Gelfond-Lifschitz transformation and defines weakly well-supported answer sets that are free of circular justifications for the class of DL-programs without negative dl-atoms. The second semantics defines strongly well-supported answer sets which are free of circular justifications for all DL-programs. We show that the existing answer set semantics for DL-programs, such as the weak answer set semantics, the strong answer set semantics, and the FLP-based answer set semantics, satisfy neither the weak nor the strong well-supportedness condition, even for DL-programs without negative dl-atoms. This explains why their answer sets incur circular justifications.