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We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be EXPTIME-complete on general structures. Finally, we show how for a specific class of structures NEXPTIME-completeness for these problems under strict semantics can be achieved., Comment: Correction of MFCS 2015 paper

In this work, we present LoCo, a fragment of classical first-order logic carefully tailored for expressing technical product configuration problems. The core feature of LoCo is that the number of components used in configurations does not have to be finitely bounded explicitly, but instead is bounded implicitly through the axioms. Computing configurations is equivalent to the task of model finding. We present the language, related algorithms, and complexity results as well as a prototypical implementation via answer set programming.

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If in contrast, the set of propositional operators is restricted, the complexity may decrease. This article systematically studies the model-checking problem for LTL formulae over restricted sets of propositional and temporal operators. For almost all combinations of temporal and propositional operators, we determine whether the model-checking problem is tractable (in PTIME) or intractable (NP-hard). We then focus on the tractable cases, showing that they all are NL-complete or even logspace solvable. This leads to a surprising gap in complexity between tractable and intractable cases. It is worth noting that our analysis covers an infinite set of problems, since there are infinitely many sets of propositional operators.

In the past few years, generalized operators (a. k. a. leaf languages) in the context of polynomial-time machines, and gates computing arbitrary groupoidal functions in the context of Boolean circuits, have raised much interest. We survey results from both areas, point out connections between them, and present relationships to a generalized quantifier concept from finite model theory.

We explore the potentially "off-by-one" nature of the definitions of counting (#P versus #NP), difference (DP versus DNP), and unambiguous (UP versus UNP; FewP versus FewNP) classes, and make suggestions as to logical approaches in each case. We discuss the strangely differing representations that oracle and predicate models give for counting classes, and we survey the properties of counting classes beyond #P. We ask whether subtracting a #P function from a P function it is no greater than necessarily yields a #P function.