This paper tries to identify the basic problems e.countered in automated theorem proving in many-valued logics and demonstrates to which extent they call be currently solved. To this end a .umber of recently developed techniques are reviewed. We list. tile avenues of research in manyvalued theorem proving that are in our eyes the most promising.

pliquées de Grenoble) with highest honours.

Freek Wiedijk proposed the well-known theorem about the irrationality of √ 2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]). This represents an important shift of emphasis in the field of automated deduction away from the somehow artificial problems of the past as represented, for exa...

A general method of automated modal logic theorem proving is discussed and illustrated. This method is based on the sub-stitutional framework for the development of systems for hybrid reasoning. Sentences in modal logic are translated into a constraint logic in which the constraints represent the connections between worlds in the possible world semantics for modal logic. Deduction in the constr...

Real-Time Graphical Interval Logic is a modal logic for reasoning about time in which the basic modality is the interval. The logic differs from other logics in that it has a natural intuitive graphical representation that resembles the timing diagrams drawn by system designers. We have developed an automated deduction system for the logic, which includes a theorem prover and a user interface. ...

An infinite sequence ∆ = 〈∆n(x0, . . . , xn−1, y, ū) : n < ω〉 of possibly infinite sets of formulas in n + 1 variables x0, . . . , xn−1, y and a possibly infinite system of parameters ū is a parameterized graded deduction-detachment (PGDD) system for a deductive system S over a S-theory T if, for every n < ω and for all φ0, . . . , φn−1, ψ ∈ FmΛ, T, φ0, . . . , φn−1 `S ψ iff T `S ∆n(φ0, . . . ,...

einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys the normalization property. To do so, we first rephrase set theory as a theory of pointed graphs (following a paradigm due to P. Aczel) by interpreting set-theoretic equality as bisimilarity, and show that in thi...

In previous works, we have introduced the notion of abstract strategies for abstract reduction systems and de ned adequate properties of termination, con uence and normalization under strategies. Thanks to this abstract strategy concept, we draw a parallel between strategies for computation and strategies for deduction. Then, deduction rules can be viewed as rewrite rules, a deduction step as a...