One of the main areas in knowledge representation and logic-based artificial intelligence concerns logical formalisms that can be used for representing and reasoning with concepts. For almost 30 years, since research in this area began, the issue of intensionality has had a special status in that it has been considered to play an important role, yet it has not been precisely established what it means for a logical formalism to be intensional. This thesis attempts to set matters straight. Based on studies of the main contributions to the issue of intensionality from philosophy of language, in particular the works of Gottlob Frege and Rudolf Carnap, we start by defining when a logical formalism is intensional. We then examine whether the current formalizations of concepts are intensional. The result is negative in the sense that none of the prevalent formalizations are intensional. This motivates the development of intensional logics for concepts. Our main contribution is the presentation of such an intensional concept logic. The intensional concept logic is a development of the well-known description logic ALC. More precisely, the logic is based, not only on a single, but on two equivalence relations. This allows us to express that concepts are co-extensional as well as to express that concepts are co-intensional. The intensional semantics of the logic is a novel algebraic semantics which is defined through abstraction of the extensional semantics of ALC . It is shown that this approach generalizes to other logics than description logics. In Danish: Et af hovedområderne inden for vidensrepræsentation og logikbaseret kunstig intelligens omhandler logiske formalismer, der er velegnede til at repræsentere begreber og til at foretage logiske slutninger, som involverer begreber. I næsten 30 år, siden forskning i dette emne begyndte, har problemstillingen intensionalitet haft en særstatus, idet den er blevet betragtet som værende vigtig, alligevel er det ikke blevet præcist fastlagt, hvad det vil sige, at en logisk formalisme er intensionel. Denne afhandling forsøger at råde bod på dette. Med udgangspunkt i hovedbidragene til intensionalitet, der stammer fra Gottlob Frege og Rudolf Carnap, starter vi med at definere, hvornår en logisk formalisme er intensionel. Derefter undersøger vi, hvorvidt de nuværende formaliseringer af begrebsviden er intensionelle. Resultatet er negativt, idet ingen af de fremherskende formaliseringer er intensionelle. Dette motiverer udviklingen af intensionelle logikker, der kan håndtere begrebsviden. Denne afhandlings hovedbidrag er en præsentation af en sådan intensionel begrebslogik. Den intensionelle begrebslogik er en videreudvikling af den velkendte beskrivelseslogik ALC . Den intensionelle logik er baseret på ikke alene ´en, men to ækvivalensrelationer, hvorved vi både kan udtrykke, at begreber har samme ekstension, samt at begreber har samme intension. Den intensionelle semantik er en ny algebraisk semantik, der er defineret ved generalisering af den ekstensionelle semantik af ALC . Det vises, at denne fremgangsmåde kan generaliseres til andre logikker.