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%From: Andre Fuhrmann <PIFUHRMA@NYX.UNI-KONSTANZ.DE>
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%                  LogIn
% Konstanz Colloquium in Logic and Information
%              5 - 7 October
%            Konstanz, Germany
%
%               ABSTRACTS
%
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   (#2)}\nopagebreak\\[1ex]\centering{\em
   #3}\nopagebreak\\[2ex]}}

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\begin{document}



\framebox{\begin{minipage}{\textwidth}
{\rule[-5mm]{0mm}{15mm}\LARGE\bf {\Huge\bf L}og{\Huge\bf I}n
\vspace{2ex} \hfill \Large Konstanz Colloquium in\\[-2.2ex]
\hspace*{\fill} Logic and Information\\[0.6ex]
\hspace*{\fill} October 5--7, 1992}\end{minipage}}\vspace{2.5ex}

\begin{center}

\LARGE\em Abstracts

\end{center}

\talk{Gabriella Crocco}{Toulouse}{to be announced}


\talk{Janusz Czelakowski}{\L odz}{On Formal Action Theory}
%
%
A formal astochastic scheme of action theory which stems from dynamic
logic, formal linguistics and deontic logic is presented. It
encompasses the well-known approaches to action (Segerberg, Nowakowska
{\em et alii\/}). A discrete {\em elementary action system\/} is a
triple

\begin{center}
(*) \qquad $(W,R,${\bf A}$)$
\end{center}

where $W$ is a set of {\em states\/}, $R$ is a binary relation on $W$
called the {\em direct transition relation\/} between states, and {\bf
A} is a non-empty family of binary relations on $W$. The members of
{\bf A} are called {\em atomic actions\/} of the system (*). Various
possible interpretations of (*) are discussed. A {\em compound
action\/} (over (*)) is a set of finite sequences of atomic actions
from {\bf A}. Every compound action can be thus viewed as a formal
language over the alphabet {\bf A}. A {\em situational action system\/}
is an extension of an elementary action system which additionally takes
into account the situational context in which actions are performed. A
situational conception of performability af actions is presented. The
relationship between action theory and deontic logic is also discussed.



\talk{J\"urgen Dix}{Karlsruhe}{Semantics of Logic Programs:
Classifying and Representing them\\by Means of Abstract Properties}
%
%
In previous work on normal programs, we have associated to any
semantics a nonmonotonic entailment relation ``$\snake$'' and considered
its abstract properties. We  have shown that  two important properties,
known in the context of nonmonotonic logics, turned out to be useful:
{\em Cumulative\/} and {\em Rational Monotony\/}. Among all known
semantics, only the wellfounded semantics WFS satisfies both properties.

Our aim in this talk is twofold:

\begin{enumerate}
\item We extend this classification  to disjunctive
programs, and

\item We present a set-up which makes it possible to prove statements
of the following kind: Any {\em reasonable\/} semantics satisfying
certain properties is uniquely determined by these.
\end{enumerate}

To this end, we  first list some new conditions that should be
satisfied by any  semantics: {\em Relevance\/}, {\em Modularity\/},
{\em Reduction\/}, {\em Isomorphy\/} and {\em PPE\/}. A semantics
satisfying these (and some more properties) is called {\em
reasonable\/}. We then present a semantical framework ${\cal M}_{NF}$
for defining and comparing semantics of logic programs. This framework
is weak enough to represent all of the  known semantics of logic
programs, including semantics based on Clark's completion. It can be
strengthened to  ensure  that any  semantics coincides with the
supported semantics of Apt, Blair and Walker when restricted to
stratified programs. The system is still weak enough to represent all
known extensions of  the supported semantics. We argue, that any
reasonable semantics fits into our framework.



\talk{Luis Fari\~nas, Andreas Herzig \ Jerome
Lang}{Toulouse}{Conditionals and Nonmonotonicity}
%
%
P. G\"ardenfors and D. Makinson showed in a recent paper that
nonmonotonic inference relations can be generated from some uncertainty
valuations on formulas. Following this approach we include the
uncertainty valuations in the language by introducing a conditional
operator, and extend their definition of nonmonotonicity. This permits
to define effective procedures for computing nonmonotonic inferences.




\talk{Sven Ove Hansson}{Uppsala}{Hidden Structures of Belief}




\talk{Andreas Herzig \ Luis Fari\~nas}{Toulouse}{Constructive
Minimal Changes}
%
%
We discuss the concepts of revision and update which have been proposed
in the literature as candidates for change operations. We argue that
updates are computationally more tractable than revisions, but both do
not give us precise information about those formulas surviving a change.

We define a semantics based on the notion of minimal change between
interpretations (as that of M. Winslett), where no meta-linguistical
information (as used e.g. by H. Katsuno and A. Mendelzon) about
dependencies or integrity constraints are used. This semantics permits
to represent the change operation in the language by a conditional
operator. We give an axiomatization which is complete for clausal
change formulas. Finally we give a proof procedure which is not based
on the explicit construction and modification of models, but on normal
forming.



\talk{Sten Lindstr\"om}{Ume\aa}{The Ramsey Test and the
Indexicality of Conditionals\\A Proposed Resolution of
G\"ardenfors' Paradox}
%
%
Working within the AGM approach, Peter G\"ardenfors has proved
that---given certain auxiliary assumptions---there are no
non-trivial belief revision systems that satisfy both the {\em
Ramsey test\/} and the {\em Preservation condition\/}.

There are various ways of reacting to G\"ardenfors' paradoxical
result. G\"ardenfors himself has described his result as a dilemma:
we must give up either the Ramsey test or the Preservation
condition. Isaac Levi has pointed to an imlicit assumption in
G\"ardenfors' approach: that conditionals express truth-value
bearing propositions and therefore are eligible as members of belief
sets. Here, we shall focus on another implicit assumption: that a
conditional sentence $A > B$ expresses one and the same proposition
with respect to every belief state. We shall argue that, contrary to
this assumption, epistemic conditionals are naturally interpreted as
{\em context-sensitive:} an epistemic conditional expresses a
proposition, but only relative to a belief state.

According to the approach advocated here, a sharp distinction is
made between the semantic level containing propositions and belief
states and the linguistic level containing sentences and sets of
sentences. Belief revision is seen as an operation on belief states;
and it is primarily propositions rather than sentences that are
accepted relative to belief states. The propositional versions of
G\"ardenfors' axioms for belief revision are shown to be consistent
with the following ``context-sensitive'' version of the Ramsey test:

(P-Ramsey) \ \ $P \Rightarrow_S Q$ is accepted in the belief
state $S$ iff $Q$ is accepted in $S*P$,

where $P$ and $Q$ are propositions. We also show how to accomodate
the full Ramsey test for conditional $sentences$, thus allowing for
unlimited iteration of conditionals.


\talk{David Makinson}{Paris}{Defeasibility, Nonmonotony, and
Failure of Modus Ponens:\\the Interconnections}
%
%
>From a naive perspective, modus ponens and monotony for a conditional
connective (or inference relation) seem to say much the same thing. Yet
we know from the logic of countefactuals that one may fail whilst the
other succeeds. One purpose of this talk is to look closely at the divorce
and show that there remain certain intimate connections. In the process
of doing so we make use of a new concept, of ``tt-monotony''. Another
purpose of the talk is to examine the relationship between formal
concepts such as these and the general informal notion of defeasibility.
In the process, we shall contend that counterfactuals of ordinary
discourse, like indicative conditionals, may be or less ``strict'' or
on the contrary exception-permitting, and that the Stalnaker/Lewis
analysis of counterfactuals favours the former at the expense of the
latter. We also suggest a natural way of transcending this limitation.




\talk{Michael Morreau}{Stuttgart}{Two Sources of Defeasibility}
%
%
Generic and dispositional statements like {\em lions eat red meat\/}
and {\em Dave is brave\/} give rise to expectations about the diets
of particular lions, and about Dave's behaviour on particular
occasions. They do so defeasibly: any particular lion is expected to
eat read meat only so long as information to the contrary is not
available.

Two views of what such sentences mean can be distinguished. One is
that they quantify universally over prototypical individuals of
various kinds. On the other view they express default
rules---licenses to draw conclusions or, to borrow Gilbert Ryle's
term, {\em inference tickets\/}. These two views are often thought to
amount to much the same thing; in this talk I argue that there are
important differences between them.

First I define the notion of an {\em inference ticket theory\/} of
defeasible reasoning, and give Reiter's Default Logic as an example.
Then I define the notion of a {\em prototype theory\/}, and give as
an example recent analyses of generics and dispositionals in
conditional logic.

Finally I show that prototype theories are at best trivial inference
ticket theories.


\talk{Ewa Orlowska}{Warsaw}{Relational Semantics for Nonclassical
Logics: Formulas are Relations}
%
%
A semantics is presented for nonclassical logics whose possible world
semantics involves binary or ternary accessibility relations. The semantics
is defined in terms of algebras of relations and it is one-sorted in the
sense that both formulas and accessibility relations are interpreted as
relations of the same rank.

Proof theory for logics with the relational semantics is outlined.

Algebraic aspects of the relational semantics are discussed and various
classes of non-classical relation algebras are defined.

Algebraic correspondence theory is suggested for further work analogous
to the correspondence theory for non-classical logics.



\talk{David Pearce}{Berlin}{Constructive Logic and Nonmonotonic
Reasoning}
%
%
Most of the systems of NMR developed in AI are supraclassical, taking
classical logic as an underlying, monotonic basis. This places the full
burden of solving problematic cases of commen-sense inference on the
specifically nonmonotonic features of the system, blurring the
distinction between problems that require a constructive formalisation,
and those which do not. This paper pleads for the usefulness of
nonmonotonic logics based on constructive logics with strong negation.
As an illustration of the general methodology, we present
``Constructive Default Logic'', whose extensions are closed under
constructive rather than classical deduction. One consequence is that
the relevant defaults can be read as ordinary (object language)
implications. Another is that the system is in close agreement with
NMR-formalisms drawn from areas like logic programming and deductive
databases, where the ``classical'' paradigm has alreaday been abandoned.



\talk{Wlodzimierz Rabinowicz}{Uppsala}{Is Preservation Worth
Preserving?}
%
%
G\"ardenfors and Makonson have recently suggested that non-monotonic
inference could be understood in terms of a hypothetical revision of the
underlying belief set. Then we can use the standard G\"ardenfors axioms
on belief revision in order to generate the logic of non-monotonic
inference. Since this kind of inference is supposed to work by default
and therefore yield somewhat provisional conclusions, its reduction to
belief revision presupposes that we interpret beliefs rather weakly: as
what G\M call ``expectations'', and not as firm beliefs or certainties.
it is clear that expectations, which are assumed to be closed under
conjunction, are something else than high probabilities. We might
perhaps understand them as those opinions that we in a given context
more or less provisionally ``take for granted'' for the purposes of
deliberation and action.

However, given this conception of belief, there is no reason to expect
that the standard belief-revision axioms are going to hold. In
particular, Preservation doesn't apply to the revision of what we take
for granted. Nor is Conservativeness going to be valid. (Similar remarks
apply to the interpretation of beliefs as those opinions that enjoy
sufficient inductive support.)

One way to deal with this problem, recently suggested by Fuhrmann and
Levi, is to use a stronger interpretation of beliefs, for which the
axioms continue to be valid, and instead modify (= complicate) the
connection between belief revision and non-monotonic inference. Another
alternative would be to give up the standard axioms on belief revision.
Question: Can we give up thesse axioms and still define belief revision
in terms of an entrenchment ordering among sentences? Is it enough to
weaken the entrenchment axioms accordingly? I will argue that this is
not as easy to do as one might expect.




\talk{Mark Ryan}{London}{Belief Revision and Ordered Theory
Presentations}
%
%
In the AGM theory of belief revision, belief states are represented by
deductively closed sets of sentences. We propose a system in which
belief states are represented by finite ordered sets of sentences,
called Ordered Theory Presentations. The sentences may be mutually
inconsistent, and the ordering means "takes priority over". We give a
syntax and semantics for OTPs. We define a natural revision function
on OTPs, which is very simple. OTPs are expressive enough to contain
information about entrenchment (again, in a simple way), which means
that iterated or repeated revision is automatically defined.

We rewrite the AGM postulates in a slightly more general way to check
which ones are satisfied by the proposed function, and find that all
but K4 and K8 are. We present both technical and intuitive arguments
against these postulates, and many examples.

In the talk, applications of OTPs to default reasoning will also be
described.


\talk{Karl Schlechta}{Stuttgart}{Completeness and Incompleteness
Results for Preferential Structures}
%
%
Shoham has generalized the Minimal Model Semantics for Circumscription
to Preferential Models. These are - like Kripke structures - sets of
classical models with a binary relation $<$. Such a structure defines a,
in general non-monotonic, consequence relation by

\begin{center}
    $a$ implies $b$  iff  in all $<$-minimal models of $a$ holds $b$.
\end{center}

Kraus, Lehmann, and Magidor have shown a number of important completeness
results for finite sets of formulas, which, however, do not always generalize
to infinite sets of formulas.

We shall examine several combinatorial completeness results which also hold
in the general infinite case, together with their logical consequences.



\talk{Krister Segerberg}{Uppsala}{to be announced}



\talk{Gerd Wagner}{Berlin}{Logics Based on Knowledge Representation
Systems}
%
%
Standard logics can be viewed as knowledge representation systems.
But usually they are too much idealised, and thus not really useful
for the purpose of real-world (non-mathematical) knowledge
representation. I discuss the theoretical requirements for knowledge
representation (restricted reflexivity, cumulativity, definiteness,
non-explosiveness, weak negation and the CWA), as well as several
examples of systems satisfying these requirements. These systems are
all related to Belnap's four-valued and Nelson's paraconsistent
constructive logic. They can be used as the theoretical basis for
extending the knowledge representation framework of database systems
and logic programming.


\talk{Heinrich Wansing}{Amsterdam}{Sequent Systems for Various
Normal Modal Propositional Logics}
%
%
As Segerberg (Bull \ Segerberg 1984) has observed, ``Gentzen methods
heve never really flourished in modal logic, but some work has been
done, mainly on sequent formulations''. In this talk I shall first
briefly review a few known sequent-style proof systems for normal modal
propositional logics and discuss the problem of Gentzenizing modal
logic from a methodological point of view. Subsequently, I shall
introduce a (slight) modification of Belnap's Display Logic and show
how this proof-theoretic framework allows for cut-free sequent calculus
presentations of various normal modal propositional logics.\footnote{All
abstracts as sent in by \today}


\end{document}

