Syllogistic Knowledge Bases with Description Logic Reasoners

Reasoning is a core topic both for natural intelligence and for artificial intelligence. While syllogistic logics (SLs) are often studied by cognitive scientists for understanding human reasoning, description logics (DLs) are usually studied by computer scientists for performing automated reasoning. Although the studies on both of these logics are extensive, their literatures are interestingly isolated from each other. Firstly, we formally define a practical family of SLs with different levels of expressivity, including a logic which has recently been introduced for automated reasoning. Then, we reveal their theoretical properties either by defining direct algorithms for deductive reasoning or by translation rules for them into relevant DLs. These algorithms and rules prove that (i) two of our SLs (namely PolSyl and NegSyl) are tractable fragments of DLs, and (ii) other two SLs (namely ComSyl and ComSyl+) are categorical fragments of DL ALC and DL ALCO with general TBoxes, respectively. These findings bridge the gap between (ancient) SLs and (modern) DLs. An immediate result is that it is possible to combine powerful features of both logics, for example, intuitional user interface of an SL and efficient reasoning algorithms for a DL. Finally, we propose a framework for knowledge representation in SLs and link it to sound and complete DL reasoners for automated deduction.