Представление рассуждений на основе публичных объявлений как частного случая абдукции

Представление рассуждений на основе публичных объявлений как частного случая абдукци

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Intuitionistic layered graph logic

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give soundness and completeness theorems for labelled tableaux and Hilbert-type systems with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent a range of systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied

Dynamic Tableaux for Dynamic Modal Logics

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. This dissertation focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language

Knowing what to do:A logical approach to planning and knowing how

In dit proefschrift wordt vanuit logisch perspectief het maken van plannen en procedurele kennis (weten hoe) onderzocht. Conformant planning is het proberen te vinden van een plan om een doel te bereiken. Doelgerichte procedurele kennis betekent dat je weet wat je moet doen om een doel te bereiken. In dit proefschrift wordt een logisch raamwerk gepresenteerd waarin de veranderende kennis van een agent gevangen kan worden. Met dit logische raamwerk, kunnen de doelen opgevat worden als logische formules. In dit proefschrift worden ook doelgerichte procedurele kennis gemodelleert. Geïnspireerd door het idee van planning, worden in dit proefschrift verschillende soorten procedurele kennis onderscheiden, zoals in termen van conformant plans en in termen van strategieën. Met behulp van logische systemen voor deze noties, worden elementaire eigenschappen voor iedere soort procedurele kennis onderzocht. Het helpt ons ook om te zien welke eigenschappen de verschillende noties van procedurele kennis gemeen hebben en welke eigenschappen uniek zijn voor iedere notie van procedurele kennis

KE Tableaux for Public Announcement Logic

Public announcement logic (PAL) is a simple dynamic epistemic logic extending reasoning about knowledge of agents with a modal operator for simultaneous and transparent knowledge updates. This logic is no more expressive than epistemic logic (EL) without updates, but exhibits compact representation of a number of complex epistemic situations. A labeled tableau proof system to reason with these updates directly is presented here. This system can analyse and present well-known epistemic puzzles like ‘muddy children ’ and ‘three wise men’. Using the KE tableau system as a basis, the modal and propositional characteristics of epistemic updates can be separated. Key words: Public announcement logic; epistemic logic; KE; semantic tableaux