Over the last 25 years, a lot of work has been done on seeking for decidable nonregular extensions of Propositional Dynamic Logic (PDL). Only recently, an expressive extension of PDL, allowing visibly pushdown automata (VPAs) as a formalism to describe programs, was introduced and proven to have a satisfiability problem complete for deterministic double exponential time. Lately, the VPA formali...

Extensions of propositional dynamic logic (PDL) with nonregular programs are considered. Three classes of nonregular languages are defined, and for each of them it is shown that for any language L in the class, PDL, with L added to the set of regular programs as a new program, is decidable. The first class consists of the languages accepted by pushdown automata that act only on the basis of the...

This paper introduces a new method for gathering unstructured workflow definition data in order to model it in relational databases. In addition to introducing an open database model, a solution has been developed to facilitate the process of defining the workflow data for process designers. This solution consists of the Process Definition Language (PDL), pre-processing of unstructured workflow...

The status of the periodontal ligament (PDL) and of the pulp are decisive for the healing of avulsed and replanted teeth. A tooth rescue box was developed and distributed to offer optimal storage conditions for avulsed teeth. The therapy comprised extraoral endodontic treatment and applications of medicaments to enhance periodontal healing. In this long-term clinical study the healing results f...

We present a (co)algebraic treatment of iteration-free dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL), both without star. The main observation is that the program/game constructs of PDL/GL arise from monad structure, and the axioms of these logics correspond to certain compatibilty requirements between the modalities and this monad structure. Our main contrib...

The performance description language PDL provides a compact notation for the speciication of non-functional attributes of VLSI systems. This paper presents evaluation mechanisms which allow the designer to assert performance goals on PDL models of VLSI systems and determine if the constrained models are satissable. This is done by developing a PDL performance model and constructing a constraint...

Propositional dynamic logic (PDL) is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, as long-known, reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL...

Pulsed dye laser (PDL) treatment is well established and has been reported to be safe and effective in the management of superficial hemangiomas, port-wine stains, and other vascular lesions. Although hyperpigmentation is quite common, other side effects such as hypopigmentation, ulceration, hemorrhaging, atrophic scarring, and hypertrophic scarring are rare. We report the case of a 42-year-old...

Propositional dynamic logic (PDL) is complete but not compact. As a consequence, strong completeness (the property Γ |= φ ⇒ Γ ` φ) requires an infinitary proof system. In this paper, we present a short proof for strong completeness of PDL relative an infinitary proof system containing the rule from [α;βn]φ for all n ∈ N, conclude [α;β∗]φ. The proof uses a universal canonical model, and it is ge...

We formally verify consistency aspects of the rule-based expert system of IBM’s System Automation software for IBM’s e-server zSeries. Starting with a formalization of the expert system in propositional dynamic logic (PDL), we are able to encode termination and determinism properties. To circumvent direct proofs in PDL or its extension PDL, we further translate versions of the occurring decisio...