Abstract.We investigate the formal specification of the reasoning process of knowledge-based systems in this paper. We analyze the corresponding parts of the KADS specification languages KARL and (ML) 2 and deduce some general requirements. The essence of these languages is that they integrate a declarative specification of inferences with control information. The languages differ in the way they achieve this integration and each of them has shortcomings. We propose a unifying semantical framework that integrates the core of the different solutions and overcomes their problems. We define a semantics and axiomatization with the Modal Change Logic (MCL). The main contribution of the paper is not to introduce yet another specification language. Instead we aim at four goals: (1) defining a framework for describing the dynamic reasoning behavior of knowledge-based systems which integrates existing approaches; (2) defining a semantics for the specification of the dynamic reasoning behavior of a knowledge-based system within the states as algebras setting that overcomes several shortcomings and ad-hoc solutions of existing approaches; and (3) providing an axiomatization that enables the development of mechanized proof support. (4) Through conceptual and semantical clarity, we investigate the relationships to similar work in software engineering and database engineering opening possibilities for further cross-fertilization of these fields.
Propositional dynamic logic (PDL) is complete but not compact. As a consequence, strong completeness (the property | ϕ ⇒ ϕ) requires an infinitary proof system. In this paper, we present a short proof for strong completeness of PDL relative to an infinitary proof system containing the rule from [α; β n ]ϕ for all n ∈ N, conclude [α; β * ]ϕ. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. Also, we show that the universal canonical model of PDL lacks the property of modal harmony, the analogue of the Truth lemma for modal operators.
In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke-Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule. 1 Motivation This paper is part of a systematic investigation of syntactical predicates based on proof theoretic methods. In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate, interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke-Feferman with its intended semantics. The method we apply is a variation of Schütte's based on infinitary proof systems. The conception of truth we investigate is a version of Kripke's theory. Kripke made use of inductive definitions in order to characterize fixed-points as intended interpretations of the truth predicate. Of special interest for Kripke is the minimal fixed-point. We will use an infinitary proof system for which the set of theorems coincides with the minimal fixed-point. One part of our investigation designs an infinitary proof system, SK ∞. The system SK ∞ is a sequent calculus with an ω-rule and truth introduction rules. With SK ∞ we can characterize the minimal strong Kleene fixed-point, I sk. In a second part we consider an internal axiomatization of the semantical theory; the resulting thoery is called PKF. This theory is a good candidate and does not contain an infinitary rule, however it is not based on classical logic but on partial logic. The system PKF was introduced by Halbach & Horsten [11] for achieving a faithful axiomatiza-tion of Kripke's fixed-point construction of Strong Kleene. The theory PKF has several interesting features for our purposes. On the one hand PKF is close to the semantic construction as it directly incorporates the closure conditions of the fixed-points. Moreover PKF is true in and only in the fixed-point models as an adequacy result shows. On the other hand PKF is close to the infinitary system SK ∞ as it can be embedded into it in a straight way. A closer look at 1
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