This paper studies a new classical natural deduction system, presented as a typed calculus named λμlet. It is designed to be isomorphic to Curien-Herbelin’s λμμ̃-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is ...

The KeY system is a development of the ongoing KeY project, whose aim is to integrate formal specification and deductive verification into the industrial software engineering processes. The deductive component of the KeY system is a novel interactive/automated prover for first-order Dynamic Logic for Java. The KeY prover features a userfriendly graphical interface, a backtracking-free free-vari...

LogAnswer is an open domain question answering system which employs an automated theorem prover to infer correct replies to natural language questions. For this purpose LogAnswer operates on a large axiom set in first-order logic, representing a formalized semantic network acquired from extensive textual knowledge bases. While other work in the field of question answering focuses on shallow lin...

This is a companion paper to [6] where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geom...

This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality whichèncodes' the new structural rules. Logics 1 1. Logics Logic is about valid deduction. One central result in logic is the deduction theorem. A; ` B if and only if`A ! B This result t...

a new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. we use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. then, we linearized this identified model at each sampling time to have an approximate linear time varying system. in order to stabilize...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...

the kind of attitude to mulla sadra’s works is important in deducing his views accurately. here, there are two types of attitudes. first, the real sadra’s views are what we understand literally from his assertions. the second is that the deduction of his final ideas needs some philosophical independent judgment (ijtihad) in addition to what is understood literally from his assertions and other ...

The purpose of this communication is to outline briefly the current state of the so-called SAD system (System for Automated Deduction), present its architecture, and discus some possible ways of its further development. At that, the main attention is paid to the development of multiple language support of the SAD system as well as to the construction of SAD proof search methods, toolkit, and en...

We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λμ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a comp...