Chitta Baral
Title: Nonmonotonicity in Specifying Goals and Directives
Alexander Bochman
Title: Nonmonotonic Reasoning and Logic
Abstract (tentative): The talk will discuss several major formalisms for NMR from a single unifying viewpoint
James Delgrande
Title: What's in a Default? On the Role and Nature of Defaults in Nonmonotonic Reasoning
Marc Denecker
Title: On the Informal and Formal Semantics of Default and Autoepistemic Logic -
Default Logic Is Not a Logic of Defaults
Abstract: In 1993, Halpern critically reexamined of Default Logic, Autoepistemic Logic and the logic of Only-knowing, and pointed out several gaps in their understanding. Now, 30 years after Reiter's introduction of Default Logic, we attempt a similar enterprise. The first point to state emphatically is one that is well-known in some
regions of the NMR community and ignored in others: that Default Logic is not a logic of defaults. It is a logic of autoepistemic reasoning, or more correctly, one of its dialects. Default and Autoepistemic logic were devised to model similar kinds of reasoning patterns, patterns that can be used to express defeasible inference rules of the kind that emerge naturally from defaults. Our main goal is to revisit the intuitions of Reiter and Moore, and develop principled formalizations
for them in the context of the unifying semantic framework for DL and AEL developed in 2003 by Denecker, Marek and Truszczynski.
Didier Dubois
Title: Uncertainty theories and non-monotonic reasoning
Abstract: Non-monotonic reasoning clusters a number of logic-related formalisms
that only share the fact of lacking the monotonicity property of
classical logic. This very unspecific features cover a number of almost
unrelated calculi having various motivations, one of which being
exception-tolerant reasoning. Knowledge representation and reasoning
systems to this end have been pioneered by Dov Gabbay and Yoav Shoham,
then extensively developed by Daniel Lehmann, Judea Pearl and their
colleagues from the mid 1980 till the mid 95. There exists natural
connections between these formalisms and theories of uncertainty like
probability theory and possibility theory. The key-connection between
uncertainty theories and exception-tolerant non-monotonic inference is
the notion of conditioning, central to uncertain reasoning, and absent
from classical logic. The aim of the talk is to show that conditional
probability, once stripped from its numerical clothes, exactly
corresponds to a non-monotonic conditional assertion captured by
preferential inference of Lehmann and colleagues (without resorting to
infinitesimals). Adding rational monotony leads to a form of
conditional modelled by conditional possibility and an inference
relation captured by possibilistic logic. This approach also accounts
for a notion of accepted defeasible beliefs that is closed under
logical consequences, and closely related to theory revision, contrary
to the usual notion of probabilistic acceptance (studied especially by
the late Henry Kyburg). Connections with imprecise probability and
modal logics of belief can thus be laid bare as well. These results
support the idea that the symbolic approach to exception tolerant
reasoning stands as a backbone to probabilistic reasoning. The latter
still obeys its basic principles (like cumulativity), but in a
degenerated (numerical) form. In this sense this talk is a plea for a
unified view of symbolic and numerical approaches to exception-tolerant
reasoning.
Thomas Eiter
Title: Distributed Nonmonotonic Reasoning
Abstract: At its inception, Nonmonotonic Reasoning was more focused on a single
reasoner (i.e., agent), later than (but to a lesser extent) multiple
reasoners came into play. Many NMR systems and tools support reasoning
at a single location (from a single knowledge base), but not
distributed reasoning where knowledge bases with independent reasoners
have to be interlinked. Given the growing importance of combining
knowledge from different, dispersed and possibliy heterogenous sources,
frameworks and platforms for distributed non-monotonic reasoning are an
interesting subject to be addressed.
Dov Gabbay (will not be able to attend)
Title: Reactivity and nonmonotonicity
Michael Gelfond
Title: The Development of Logic Programming Based KR Languages - a Personal Perspective
Georg Gottlob
Title: From the complexity of nonmonotonic logics to Datalog+-
Michael Kaminski
Title: First-order non-monotonic logics: a unified approach
Abstract: We consider the first-order versions of propositional non-monotonic
logics. The definition of these logics is based on an equivalent
semantical description of propositional default, (ground) non-monotonic
modal, and autoepistemic logics. An important feature of this
definition is a unified approach to all above mentioned first-order
non-monotoniclogics. Thus, in particular, first-order (ground)
non-monotonic modal and autoepistemic logics well comply with
first-order default logic, providing a substantial evidence for their
adequacy. In addition, first-order nonmonotonic logics possess many of
the basic properties of their propositional counterparts, which
supplies an additional support to their appropriateness.
Daniel Lehmann
Title: Nonmonotonic logics without and with connectives
Abstract: Abstract: Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson’s early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of Sen’s property α. The representation results obtained are surprisingly smooth: in the completeness part the choice function may be defined on any set of worlds, not only definable sets and no definability- preservation property is required in the soundness part. For abstract cumulative logics, proper conjunction and negation may be defined. No proper disjunction seems to be definable in general. Quantum Logic and its negation are also discussed.
Nicola Leone
Title: ASP with Function Symbols: Overview and Perspectives
Vladimir Lifschitz
Title: Circumscription Has Two Daughters
Abstract: Circumscription, born in 1980, adopted two children: a baby,
named Nonmonotonic Causal Logic, in 1997, and a teenager, Stable Model
Semantics, in 2007.
Jack Minker
Title: Reminiscences on Nonmonotonic Reasoning
Ilkka Niemela Title:
David PearceTitle: The Gödel and the Splitting Translations
Abstract: When the new research area of logic programming and
non-monotonic reasoning emerged at the end of the 1980s, it focused
notably on the study of mathematical relations between different
non-monotonic formalisms, especially between the semantics of stable
models and various non-monotonic modal logics. Given the many and varied
embeddings of stable models into systems of modal logic, the modal
interpretation of logic programming connectives and rules became the
dominant view until well into the new century. Recently, modal
interpretations are once again receiving attention in the context of
hybrid theories that combine reasoning with non-monotonic rules and
ontologies or external knowledge bases.
In this
talk I explain how all of the familiar embeddings of stable models into
modal logics can be seen as special cases of two translations that are
very well-known in non-classical logic. They are, first, the
translation used by Gödel in 1933 to embed Heyting's intuitionistic
logic H into a modal provability logic equivalent to Lewis's S4; second,
the splitting translation, known since the mid-1970s, that allows one
to embed extensions of S4 into extensions of the non-reflexive logic,
K4. By composing the two translations one can obtain (Goldblatt, 1978)
an adequate provability interpretation of H within the Gödel-Löb logic
GL, the system shown by Solovay (1976) to capture precisely the
provability predicate of Peano Arithmetic. These two translations and
their composition not only apply to monotonic logics extending H and S4,
they also apply in several relevant cases to non-monotonic logics built
upon such extensions, including equilibrium logic, non-monotonic S4F
and autoepistemic logic. The embeddings obtained are not merely faithful
and modular, they are based on fully recursive translations applicable
to arbitrary logical formulas. Besides providing a uniform picture of
some older results in LPNMR, the translations yield a perspective from
which some new logics of belief emerge in a natural way.
Jeffrey Remmel Title: Extensions of Answer Set
Programming
Abstract: We will survey several extensions of the ASP paradigm. These include adding set based constraints to ASP and their applications to expressing
preferences in a ASP setting, set based logic programming with
applications to reasoning about infinite sets, and a more recent
extension which we call Hybrid ASP with applications to reasoning about
continuous trajectories.
Erik Sandewall
Title: Early history of nonmonotonic reasoning
Torsten Schaub
Title: Modern Answer Set Solving
