Action, Time and Space in Description Logics

Description Logics (DLs) are a family of logic-based knowledge representation (KR) formalisms designed to represent and reason about static conceptual knowledge in a semantically well-understood way. On the other hand, standard action formalisms are KR formalisms based on classical logic designed to model and reason about dynamic systems. The largest part of the present work is dedicated to integrating DLs with action formalisms, with the main goal of obtaining decidable action formalisms with an expressiveness significantly beyond propositional. To this end, we offer DL-tailored solutions to the frame and ramification problem. One of the main technical results is that standard reasoning problems about actions (executability and projection), as well as the plan existence problem are decidable if one restricts the logic for describing action pre- and post-conditions and the state of the world to decidable Description Logics. A smaller part of the work is related to decidable extensions of Description Logics with concrete datatypes, most importantly with those allowing to refer to the notions of space and time

A Strategy for Implementing description Temporal Dynamic Algorithms in Dynamic Knowledge Graphs by SPIN

Planning and reasoning about actions and processes, in addition to reasoning about propositions, are important issues in recent logical and computer science studies. The widespread use of actions in everyday life such as IoT, semantic web services, etc., and the limitations and issues in the action formalisms are two factors that lead us to study how actions are represented. Since 2007, there have been some ideas to integrate Description Logic (DL) and action formalisms for representing both static and dynamic knowledge. Meanwhile, time is an important factor in dynamic situations, and actions change states over time. In this study, on the one hand, we examined related logical structures such as extensions of description logics (DLs), temporal formalisms, and action formalisms. On the other hand, we analyzed possible tools for designing and developing the Knowledge and Action Base (KAB). For representation and reasoning about actions, we embedded actions into DLs (such as Dynamic-ALC and its extensions). We propose a terminable algorithm for action projection, planning, checking the satisfiability, consistency, realizability, and executability, and also querying from KAB. Actions in this framework were modeled with SPIN and added to state space. This framework has also been implemented as a plugin for the Prot\'eg\'e ontology editor. During the last two decades, various algorithms have been presented, but due to the high computational complexity, we face many problems in implementing dynamic ontologies. In addition, an algorithm to detect the inconsistency of actions' effects was not explicitly stated. In the proposed strategy, the interactions of actions with other parts of modeled knowledge, and a method to check consistency between the effects of actions are presented. With this framework, the ramification problem can be well handled in future works

Modelling Learning as Modelling

Economists tend to represent learning as a procedure for estimating the parameters of the "correct" econometric model. We extend this approach by assuming that agents specify as well as estimate models. Learning thus takes the form of a dynamic process of developing models using an internal language of representation where expectations are formed by forecasting with the best current model. This introduces a distinction between the form and content of the internal models which is particularly relevant for boundedly rational agents. We propose a framework for such model development which use a combination of measures: the error with respect to past data, the complexity of the model, the cost of finding the model and a measure of the model's specificity The agent has to make various trade-offs between them. A utility learning agent is given as an example

Synthesizing and executing plans in Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved

Plan Synthesis for Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs), a rich, dynamic framework, where states are description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that possibly introduce new objects from an infinite domain. We show that plan existence over KABs is undecidable even under severe restrictions. We then focus on state-bounded KABs, a class for which plan existence is decidable, and provide sound and complete plan synthesis algorithms, which combine techniques based on standard planning, DL query answering, and finite-state abstraction. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning

Tool support for reasoning in display calculi

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi