36 research outputs found
Generating Schemata of Resolution Proofs
Two distinct algorithms are presented to extract (schemata of) resolution
proofs from closed tableaux for propositional schemata. The first one handles
the most efficient version of the tableau calculus but generates very complex
derivations (denoted by rather elaborate rewrite systems). The second one has
the advantage that much simpler systems can be obtained, however the considered
proof procedure is less efficient
From Specifications to Behavior: Maneuver Verification in a Semantic State Space
To realize a market entry of autonomous vehicles in the foreseeable future,
the behavior planning system will need to abide by the same rules that humans
follow. Product liability cannot be enforced without a proper solution to the
approval trap. In this paper, we define a semantic abstraction of the
continuous space and formalize traffic rules in linear temporal logic (LTL).
Sequences in the semantic state space represent maneuvers a high-level planner
could choose to execute. We check these maneuvers against the formalized
traffic rules using runtime verification. By using the standard model checker
NuSMV, we demonstrate the effectiveness of our approach and provide runtime
properties for the maneuver verification. We show that high-level behavior can
be verified in a semantic state space to fulfill a set of formalized rules,
which could serve as a step towards safety of the intended functionality.Comment: Published at IEEE Intelligent Vehicles Symposium (IV), 201
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
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
Schemata of SMT problems
Session 3 (full paper)International audienceA logic is devised for reasoning about iterated schemata of SMT problems. The satisfiability problem is shown to be undecidable for this logic, but we present a proof procedure that is sound, complete w.r.t. satisfiability and terminating for a precisely characterized class of problems. It is parameterized by an external procedure (used as a black box) for testing the satisfiability of ground instances of the schema in the considered theory (e.g. integers, reals etc.)
Linear Temporal Logic and Propositional Schemata, Back and Forth
Session: p-Automata and Obligation Games - http://www.isp.uni-luebeck.de/time11/International audienceThis paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced in elsewhere 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
Decidability and Undecidability Results for Propositional Schemata
International audienceWe define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability