By Alexandre Rademaker

ISBN-10: 144714001X

ISBN-13: 9781447140016

ISBN-10: 1447140028

ISBN-13: 9781447140023

Advent -- historical past -- The Sequent Calculus for ALC -- evaluating SC ALC SC with different ALC Deduction structures -- A normal Deduction for ALC -- in the direction of an explanation thought for ALCQI -- Proofs and motives -- A Prototype Theorem Prover -- end

**Read or Download A proof theory for description logics PDF**

**Similar theory books**

**Intelligent Systems: From Theory to Practice**

This quantity incorporates a number of peer reviewed best prolonged models of papers provided at IEEE-IS’2008 complemented with a few proper works of most sensible those who haven't attended the convention. the themes coated contain almost all parts which are thought of to be proper for the advance of greatly perceived clever structures.

**Non-Noetherian Commutative Ring Theory**

Commutative Ring concept emerged as a special box of study in math ematics in basic terms at first of the 20th century. it truly is rooted in 9 teenth century significant works in quantity idea and Algebraic Geometry for which it supplied a useful gizmo for proving effects. From this humble starting place, it flourished right into a box of research in its personal correct of an fantastic richness and curiosity.

**Theory and Applications for Advanced Text Mining**

This publication consists of nine chapters introducing complex textual content mining concepts. they're a number of suggestions from relation extraction to lower than or much less resourced language. i feel that this ebook will provide new wisdom within the textual content mining box and support many readers open their new examine fields.

**Additional resources for A proof theory for description logics**

**Example text**

It is easy to see that from (1) and (2) S1 ∪ S2 |= (C1 C2 ) L α and S1 ∪ S2 |= (C1 C2 ) L β. 1 we get the desired result S1 ∪ S2 |= (C1 C2 ) L (α β). Rules -i Π1 Again by induction hypothesis, if L α is a derivation with all hypothesis in {C, S} then S |= C L α. 3 to S |= C L (α β). Rule ( -e) By induction hypothesis, if Π1 L (α β), [ L β] [ L α] Π2 Π3 γ and γ are derivations with hypothesis in {C, S}, { L α, S} and { L β, S}, respectively. Then, L (α β), S |= L α γ and S |= L β γ . 3, S |= L (α β) transitivity of set inclusion we can get the desired result S |= C γ .

Rm ,L m Bm ⇒ C1 , . . , Cl , ∃R1 ,L 1 D1 , . . 4) where we group the concepts into four sets Δ1 , Δ2 , Δ3 and Δ4 . A1,n and C1,l are sets of atomic concepts. In Δ2 , B1,m are atomic concepts or disjunctions of concepts (not necessarily atomic). In Δ4 , D1, p are atomic concepts or conjunctions of concepts (not necessarily atomic). 4), one has just to observe that: (1) the -r and -l rules provisos are blocking the decomposition of the conjunctions and disjunctions; and (2) the prom-∀ (prom-∃) rule cannot be applied due to the lack of a universal (existential) quantified concept on the right (left).

That is, ∀R occuring in front of the list of labels in Δ2 , ∃x(a, x) ∈ R I . We must mention that even if one of the concepts in Δ2 is or ⊥, we can always construct I. Case ⇒ Δ4 We can construct a counter-model such that I |= ⇒ Δ4 . From the natural interpretation of a sequent, we know that an interpretation will not satisfy this case when there is at least one element a ∈ (∃R1 ,L 1 D1 . . ∃R p ,L p D p )I . 3 Obtaining Counter-Models From Unsuccessful Proof Trees 47 sequent is interpreted as a conjunction, if empty, its semantics for any interpretation function is the universe set of the interpretation.

### A proof theory for description logics by Alexandre Rademaker

by Donald

4.4