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A paraconsistent approach to actions in informationally complex environments. (English) Zbl 07121048
The paper deals with an important issue of reasoning, planning and acting in informationally complex and dynamic environments. Due to the heterogeneity of distributed information sources of diverse quality and credibility, inconsistent and incomplete information is a common phenomenon. Hence, planning actions that would not only tolerate but also handle such situations in a tractable way is a significant issue, in particular in critical or emergency situations in our reality. To this end, the paper introduces ACTLOG, a rule-based four-valued language designed to specify actions in a paraconsistent and paracomplete manner. The language is an extension of 4QLBel, which is a language for reasoning with paraconsistent belief bases. The actions specified in ACTLOG can be conceived as the activity that transform a belief basefrom one its state too another. In contrast to other approaches, ACTLOG actions can be executed even when the underlying belief base information is inconsistent and/or incomplete. ACTLOG also makes it possible to deal with composite actions using sequential and parallel compositions as well as conditional specifications. The framework is illustrated on a decontamination case study known from the literature.
The main goal of the paper is to introduce a tool for planning actions such that it is rich enough to deal with inconsistent and incomplete information bases. An additional goal, which the paper addresses as well, is to develop actions’ specification language, adequate for reasoning and planning in informationally complex and sometimes defective environments. The authors introduce ACTLOG that makes it possible meet these goals in a computationally tractable way.
In principal, the ACTLOG language is a four-valued logic. In order to achieve the required expressiveness, tractability and modelling convenience, next to truth $$(t)$$ and falsity $$(f)$$ two additional truth values are introduced, namely inconsistent $$(i)$$ and unknown $$(u)$$. The four-valued language employs the connectives $$\neg$$, $$\wedge$$, $$\vee$$ and $$\rightarrow$$ that behave classically on classical truth values $$t, f$$. When the set of truth values is restricted to $$t, f ,u$$ or to $$t, f, i$$, the resulting logic is the well-known three-valued logic of Kleene, where the non-classical truth values represent indefiniteness, which is commonly accepted in modelling lack of knowledge, and inconsistency. ACTLOG belongs to the 4QL family of four-valued, rule-based languages. It builds on 4QLBel, which is the extension of the 4QL rule language. The doxastic extension 4QLBel operates with belief bases that consist of the so-called $$3i$$-worlds (possibly inconsistent or undefined information states) and is designed towards specifying actions.
The specification of composite actions is important in applications of the ACTLOG language. Composite actions are specified as compositions of atomic actions (with parameters) by means of the operator ‘;’ for sequential composition), $$\Rightarrow$$ for the conditional ‘if-then-else’ composition and ‘$$\Vert$$’ for parallel composition.
Summing up, ACTLOG provides a nuanced action specification tools, allowing for subtle interplay among various forms of nonmonotonic, paraconsistent, paracomplete and doxastic reasoning methods applicable in informationally complex environments.
The paper is written in a crisp and clear way, without typos. All concepts are well defined and their applications demonstrated by examples. Perhaps the only one negative comment is this. Tables should be inserted close to the point where they are referred to. It is not a good practice to insert a table among the text of another paragraph than that one that refers to it.
##### MSC:
 03B53 Paraconsistent logics 03B42 Logics of knowledge and belief (including belief change) 68N17 Logic programming 68T27 Logic in artificial intelligence
CCalc; GOLOG
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