A layered rule-based architecture for approximate knowledge fusion?

Description logics provide powerful languages for representing and reasoning about knowledge of static application domains. The main strength of description logics is that they offer considerable expressive power going far beyond propositional logic, while reasoning is still decidable. There is a demand to bring the power and character of description logics into the description and reasoning of dynamic application domains which are characterized by actions. In this paper, based on a combination of the propositional dynamic logic PDL, a family of description logics and an action formalism constructed over description logics, we propose a family of dynamic description logics DDL(X @) for representing and reasoning about actions, where X represents well-studied description logics ranging from the to the , and X @ denotes the extension of X with the @ constructor. The representation power of DDL(X @) is reflected in four aspects. Firstly, the static knowledge of application domains is represented as RBoxes and acyclic TBoxes of the description logic X. Secondly, the states of the world and the pre-conditions of atomic actions are described by ABox assertions of the description logic X @, and the post-conditions of atomic actions are described by primitive literals of X @. Thirdly, starting with atomic actions and ABox assertions of X @, complex actions are constructed with regular program constructors of PDL, so that various control structures on actions such as the "Sequence", "Choice", "Any-Order", "Iterate", "If-Then-Else", "Repeat-While" and "Repeat-Until" can be represented. Finally, both atomic actions and complex actions are used as modal operators for the construction of formulas, so that many properties on actions can be explicitly stated by formulas. A tableau-algorithm is provided for deciding the satisfiability of DDL(X @)-formulas; based on this algorithm, reasoning tasks such as the realizability, executability and projection of actions can be effectively carried out. As a result, DDL(X @) not only offers considerable expressive power going beyond many action formalisms which are propositional, but also provides decidable reasoning services for actions described by it.

Dynamic linear time temporal logic

Propositional dynamic logic with local assignment

Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator, called concurrent propositional dynamic logic (CPDL) [20], was introduced to formalise programs running in parallel. In a different direction, other authors proposed a systematic method for generating multi-valued propositional dynamic logics to reason about weighted programs [15]. This paper presents the first step of combining these two frameworks to introduce uncertainty in concurrent computations. In the proposed framework, a weight is assigned to each branch of the parallel execution, resulting in a (possible) asymmetric parallelism, inherent to the fuzzy programming paradigm [2, 23]. By adopting such an approach, a family of logics is obtained, called multi-valued concurrent propositional dynamic logics (\(\mathcal {GCDL}(\mathbf {A})\)), parametric on an action lattice \(\mathbf {A}\) specifying a notion of “weight” assigned to program execution. Additionally, the validity of some axioms of CPDL is discussed in the new family of generated logics.

Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.

In classical deterministic planning, solutions to planning tasks are simply sequences of actions, but that is not sufficient for contingent plans in non-deterministic environments. Contingent plans are often expressed through policies that map states to actions. An alternative is to specify contingent plans as programs, e.g. in the syntax of Propositional Dynamic Logic (PDL). PDL is a logic for reasoning about programs with sequential composition, test and non-deterministic choice. However, as we show in the paper, none of the existing PDL modalities directly captures the notion of a solution to a planning task under non-determinism. We add a new modality to star-free PDL correctly capturing this notion. We prove the appropriateness of the new modality by showing how to translate back and forth between policies and PDL programs under the new modality. More precisely, we show how a policy solution to a planning task gives rise to a program solution expressed via the new modality, and vice versa. We also provide an axiomatisation of our PDL extension through reduction axioms into standard star-free PDL.

We investigate the relationship amongst some solutions to the frame problem. We encode Pednault’s syntax-based solution [20], Baker’s state-minimization policy [1], and Gelfond & Lifchitz’s Action Language A [7] in the propositional dynamic logic (PDL).T he formal relationships among these solutions are given. The results of the paper show that dynamic logic, as one of the formalisms for reasoning about dynamic domains, can be used as a formal tool for comparing and unifying logics of action.Keywordsrelationships between formalismsframe problemdynamic logic

On the Computational Feasibility of Abductive Diagnosis for Practical Applications

This work presents three increasingly expressive Dynamic Logics in which the programs are described in a language based on CCS. Our goal is to build dynamic logics that are suitable for the description and verification of properties of communicating concurrent systems, in a similar way as PDL is used for the sequential case. In order to accomplish that, CCS’s operators and constructions are added to a basic modal logic. Doing this, the semantics of CCS’s parallel operator allows us to build dynamic logics that support communicating and concurrent programs. We build a simple Kripke semantics for these logics, provide complete axiomatizations for them and show that they have the finite model property. This contrasts with other dynamic logics with parallel operators presented in the literature, such as Peleg’s Concurrent PDL with Channels, where either the parallel programs cannot communicate, or at least one of the properties mentioned above (simple Kripke semantics, complete axiomatization and finite model property) is missing.

Chapter 1 Knowledge Representation and Classical Logic

In this paper, we present methods for eliminating higher-order quantifiers in proof goals arising in the verification of digital circuits. For the description of the circuits, a subset of higher-order logic called hardware formulae is used which is sufficient for describing hardware specifications and implementations at register transfer level. Real circuits can be dealt with as well as abstract (generic) circuits. In case of real circuits, it is formally proved, that the presented transformations result in decidable formulae, such that full automation is achieved for them. Verification goals of abstract circuits can be transformed by the presented methods into goals of logics weaker than higher-order logic, e.g. (temporal) propositional logic. The presented transformations are also capable of dealing with hierarchy and have been implemented in HOL90.

The dynamic description logic DDL provides formalism for describing dynamic system in the semantic Web environment Model checking is a formal verification method based on state transition system. In this paper, we bring dynamic description logic into model checking. Firstly, state transition systems considered in model checking are modeled as complex actions in dynamic description logic. Secondly, a kind of temporal description logic DL-CTL is introduced to specify temporal properties on state transition systems, where DL-CTL is a DL-based extension of propositional branch-time temporal logic CTL. Finally, verification algorithm is presented with the help of reasoning mechanisms provided by description logic.

Propositional dynamic logic of nonregular programs

Determinism and non-determinism in PDL

In this paper we attempt to shed light on the concept of an agent’s knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent logic of Semi-Public Environments (SPE). These logics represent two different approaches for defining the aforementioned actions, and in order to provide unified frameworks that encompass both, we define the logics DELVO (DEL+Vision+Ontic change) and PDLVE (PDL+Vision+Epistemic operators). DELVO is given a sound and complete axiomatisation.