BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sándor Jenei (University of Pécs) DTSTART:20210108T170000Z DTEND:20210108T190000Z DTSTAMP:20260423T035912Z UID:NCLogic/1 DESCRIPTION:Title: A representation theorem for odd and even involutive commutative residuate d chains by direct systems of abelian o-groups\nby Sándor Jenei (Univ ersity of Pécs) as part of Nonclassical Logic Webinar\n\n\nAbstract\nAlge braic investigations into substructural logics have been flourishing in th e past decades\, but the focus of this research has been fairly biased tow ards integral or idempotent or divisible structures which were already wel l-understood. On the contrary\, (quasi)varieties of not necessarily integr al and not necessarily divisible algebras form equivalent algebraic semant ics for all the main logics in the linear and in the relevant family\, inc luding Abelian logic\, and it is precisely in this area where it is possib le to find very interesting connections with (lattice ordered) groups and thus with classical algebra.\nIn this talk we address the problem of struc tural description of involutive commutative residuated lattices\, the non- integral case. The algebras in our focus are non-divisible and non-idempot ent either. Related attempts in the literature have\, so far\, been confin ed to either lattice-ordered groups (the cancellative case) or Sugihara mo noids (the idempotent case). For all involutive commutative residuated cha ins\, where either the residual complement operation leaves the unit eleme nt fixed (odd case) or the unit element is the cover of its residual compl ement (even case)\, a representation theorem will be presented in this tal k by means of direct systems of abelian o-groups.\n LOCATION:https://researchseminars.org/talk/NCLogic/1/ END:VEVENT END:VCALENDAR