3 research outputs found
Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions
Forgetting is an important concept in knowledge representation and automated
reasoning with widespread applications across a number of disciplines. A
standard forgetting operator, characterized in [Lin and Reiter'94] in terms of
model-theoretic semantics and primarily focusing on the propositional case,
opened up a new research subarea. In this paper, a new operator called weak
forgetting, dual to standard forgetting, is introduced and both together are
shown to offer a new more uniform perspective on forgetting operators in
general. Both the weak and standard forgetting operators are characterized in
terms of entailment and inference, rather than a model theoretic semantics.
This naturally leads to a useful algorithmic perspective based on quantifier
elimination and the use of Ackermman's Lemma and its fixpoint generalization.
The strong formal relationship between standard forgetting and strongest
necessary conditions and weak forgetting and weakest sufficient conditions is
also characterized quite naturally through the entailment-based, inferential
perspective used. The framework used to characterize the dual forgetting
operators is also generalized to the first-order case and includes useful
algorithms for computing first-order forgetting operators in special cases.
Practical examples are also included to show the importance of both weak and
standard forgetting in modeling and representation
Proceedings of the Automated Reasoning Workshop (ARW 2019)
Preface
This volume contains the proceedings of ARW 2019, the twenty sixths Workshop on Automated Rea-
soning (2nd{3d September 2019) hosted by the Department of Computer Science, Middlesex University,
England (UK). Traditionally, this annual workshop which brings together, for a two-day intensive pro-
gramme, researchers from different areas of automated reasoning, covers both traditional and emerging
topics, disseminates achieved results or work in progress. During informal discussions at workshop ses-
sions, the attendees, whether they are established in the Automated Reasoning community or are only at
their early stages of their research career, gain invaluable feedback from colleagues. ARW always looks
at the ways of strengthening links between academia, industry and government; between theoretical and
practical advances. The 26th ARW is affiliated with TABLEAUX 2019 conference.
These proceedings contain forteen extended abstracts contributed by the participants of the workshop
and assembled in order of their presentations at the workshop. The abstracts cover a wide range of topics
including the development of reasoning techniques for Agents, Model-Checking, Proof Search for classical
and non-classical logics, Description Logics, development of Intelligent Prediction Models, application of
Machine Learning to theorem proving, applications of AR in Cloud Computing and Networking.
I would like to thank the members of the ARW Organising Committee for their advice and assis-
tance. I would also like to thank the organisers of TABLEAUX/FroCoS 2019, and Andrei Popescu, the
TABLEAUX Conference Chair, in particular, for the enormous work related to the organisation of this
affiliation. I would also like to thank Natalia Yerashenia for helping in preparing these proceedings.
London Alexander Bolotov
September 201
Forgetting in multi-agent modal logics
International audienceIn the past decades, forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning. However, forgetting in multi-agent modal logics has largely been unexplored. In this paper, we study forgetting in multi-agent modal logics. We adopt the semantic definition of existential bisimulation quantifiers as that of forgetting. We propose a syntactical way of performing forgetting based on the canonical formulas of modal logics introduced by Moss. We show that the result of forgetting a propositional atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with >. Thus we show that Kn, Dn, Tn, K45n, KD45n and S5n are closed under forgetting, and hence have uniform interpolation