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class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability , between class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-terms and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-algebras. For each class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-algebra, the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory; we identify and investigate the complements as fragments of its universal theory. We offer characterizations of those algebras that (positively) satisfy just those terms that are satisfiable in the two-element Boolean algebra providing its semantics to classical propositional logic. In case of positive satisfiability, these algebras are just the nontrivial weakly contractive class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-algebras. In case of satisfiability, we give a characterization by means of another property of the algebra, the existence of a two-element congruence. Further, we argue that (positive) satisfiability problems in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304397516001997&_mathId=si1.gif&_user=111111111&_pii=S0304397516001997&_rdoc=1&_issn=03043975&md5=d6c872fb3967f4daf4cc72fbdb97cbce" title="Click to view the MathML source">FLewclass="mathContainer hidden">class="mathCode">-algebras are computationally hard. Some previous results in the area of term satisfiability in MV-algebras or BL-algebras are thus brought to a common footing with known facts on satisfiability in Heyting algebras.