Fuzzy Description Logics (DLs) with t-norm semantics have been studied as a means for representing and reasoning with vague knowledge. Recent work has shown that even fairly inexpressive fuzzy DLs become undecidable for a wide variety of t-norms. We complement those results by providing a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp r...

A popular score normalization technique termed T-norm is the central focus of this paper. Based on widely confirmed experimental observation regarding T-norm tilting the DET curves of speaker detection systems, we set out to identify the components taking role in this phenomenon. We claim that under certain local assumptions the T-norm performs a gaussianization of the individual true and impos...

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron’s communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand’s theorem...

CADIAG-2 is a successful expert system assisting in the differential diagnosis in internal medicine. With its aid, conjectures about present diseases are derived from possibly vague information about a patient’s symptoms. In this paper we provide a mathematical formalisation of the inferential mechanism of CADIAG-2. A Gentzen-style calculus for the resulting logic is introduced and used to comp...

The study of the Gentzen system Gew determined by the well known sequent calculus FLew [Ono98, Ono03c] is interesting for the study of the substructural aspects of t-norm based logics [Háj98, EG01]. In [BGV05] we studied the 〈∨, ∗,¬, 0, 1〉 and the 〈∨,∧, ∗,¬, 0, 1〉-fragments of this Gentzen system and the same fragments of the logic of residuated lattices IPC∗\c. In this paper we continue the st...

ΠMTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that ΠMTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of ΠMTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0, 1] generates the variety of all ΠMTL-alge...

T-norm based fuzzy logics are usually considered as truth preserving, that is, taking 1 as the only truth value to be preserved in inferences. In this paper we study t-norm based fuzzy logics preserving degrees of truth, that is, preserving the lower bounds of the truth degrees of the premises. These logics are axiomatizable by using a restricted form of Modus Ponens together with the rule of A...

We provide general conditions on hypersequent calculi that guarantee standard completeness for the formalized logics. These conditions are implemented in the PROLOG system AxiomCalc that takes as input any suitable axiomatic extension of Monoidal T-norm Logic MTL and outputs a hypersequent calculus for the logic and the result of the check. Our approach subsumes many existing results and allows...

This paper is a humble homage to Enric Trillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of these models, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics. We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence o...