3,532 research outputs found
Reasoning on Schemata of Formulae
A logic is presented for reasoning on iterated sequences of formulae over
some given base language. The considered sequences, or "schemata", are defined
inductively, on some algebraic structure (for instance the natural numbers, the
lists, the trees etc.). A proof procedure is proposed to relate the
satisfiability problem for schemata to that of finite disjunctions of base
formulae. It is shown that this procedure is sound, complete and terminating,
hence the basic computational properties of the base language can be carried
over to schemata
Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)
This paper relates the well-known Linear Temporal Logic with the logic of
propositional schemata introduced by the authors. We prove that LTL is
equivalent to a class of schemata in the sense that polynomial-time reductions
exist from one logic to the other. Some consequences about complexity are
given. We report about first experiments and the consequences about possible
improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs,
additional examples & figures, additional comparison between classical
LTL/schemata algorithms up to the provided translations, and an example of
how to do model checking with schemata; 36 pages, 8 figure
On Automating the Doctrine of Double Effect
The doctrine of double effect () is a long-studied ethical
principle that governs when actions that have both positive and negative
effects are to be allowed. The goal in this paper is to automate
. We briefly present , and use a first-order
modal logic, the deontic cognitive event calculus, as our framework to
formalize the doctrine. We present formalizations of increasingly stronger
versions of the principle, including what is known as the doctrine of triple
effect. We then use our framework to simulate successfully scenarios that have
been used to test for the presence of the principle in human subjects. Our
framework can be used in two different modes: One can use it to build
-compliant autonomous systems from scratch, or one can use it to
verify that a given AI system is -compliant, by applying a
layer on an existing system or model. For the latter mode, the
underlying AI system can be built using any architecture (planners, deep neural
networks, bayesian networks, knowledge-representation systems, or a hybrid); as
long as the system exposes a few parameters in its model, such verification is
possible. The role of the layer here is akin to a (dynamic or
static) software verifier that examines existing software modules. Finally, we
end by presenting initial work on how one can apply our layer
to the STRIPS-style planning model, and to a modified POMDP model.This is
preliminary work to illustrate the feasibility of the second mode, and we hope
that our initial sketches can be useful for other researchers in incorporating
DDE in their own frameworks.Comment: 26th International Joint Conference on Artificial Intelligence 2017;
Special Track on AI & Autonom
A Decidable Class of Nested Iterated Schemata (extended version)
Many problems can be specified by patterns of propositional formulae
depending on a parameter, e.g. the specification of a circuit usually depends
on the number of bits of its input. We define a logic whose formulae, called
"iterated schemata", allow to express such patterns. Schemata extend
propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with
generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n
is an (unbound) integer variable called a "parameter". The expressive power of
iterated schemata is strictly greater than propositional logic: it is even out
of the scope of first-order logic. We define a proof procedure, called DPLL*,
that can prove that a schema is satisfiable for at least one value of its
parameter, in the spirit of the DPLL procedure. However the converse problem,
i.e. proving that a schema is unsatisfiable for every value of the parameter,
is undecidable so DPLL* does not terminate in general. Still, we prove that it
terminates for schemata of a syntactic subclass called "regularly nested". This
is the first non trivial class for which DPLL* is proved to terminate.
Furthermore the class of regularly nested schemata is the first decidable class
to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n
(/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated
Schemata", submitted to IJCAR 200
Constructing Conditional Plans by a Theorem-Prover
The research on conditional planning rejects the assumptions that there is no
uncertainty or incompleteness of knowledge with respect to the state and
changes of the system the plans operate on. Without these assumptions the
sequences of operations that achieve the goals depend on the initial state and
the outcomes of nondeterministic changes in the system. This setting raises the
questions of how to represent the plans and how to perform plan search. The
answers are quite different from those in the simpler classical framework. In
this paper, we approach conditional planning from a new viewpoint that is
motivated by the use of satisfiability algorithms in classical planning.
Translating conditional planning to formulae in the propositional logic is not
feasible because of inherent computational limitations. Instead, we translate
conditional planning to quantified Boolean formulae. We discuss three
formalizations of conditional planning as quantified Boolean formulae, and
present experimental results obtained with a theorem-prover
Clausal Resolution for Modal Logics of Confluence
We present a clausal resolution-based method for normal multimodal logics of
confluence, whose Kripke semantics are based on frames characterised by
appropriate instances of the Church-Rosser property. Here we restrict attention
to eight families of such logics. We show how the inference rules related to
the normal logics of confluence can be systematically obtained from the
parametrised axioms that characterise such systems. We discuss soundness,
completeness, and termination of the method. In particular, completeness can be
modularly proved by showing that the conclusions of each newly added inference
rule ensures that the corresponding conditions on frames hold. Some examples
are given in order to illustrate the use of the method.Comment: 15 pages, 1 figure. Preprint of the paper accepted to IJCAR 201
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