407 research outputs found
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
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
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
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
Uncertain Reasoning in Justification Logic
This thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and completeness theorems for our logics and establish decidability procedures. Both our logics rely on an infinitary rule so that strong completeness can be achieved. One of the most interesting mathematical results for our logics is the fact that adding only one iteration of the probability operator to the justification logic J does not increase the computational complexity of the logic
Internal Calculi for Separation Logics
We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem
A Resolution Calculus for First-order Schemata
International audienceWe devise a resolution calculus that tests the satisfiability of infinite families of clause sets, called clause set schemata. For schemata of propositional clause sets, we prove that this calculus is sound, refutationally complete, and terminating. The calculus is extended to first-order clauses, for which termination is lost, since the satisfiability problem is not semi-decidable for nonpropositional schemata. The expressive power of the considered logic is strictly greater than the one considered in our previous work
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