相关论文: Decision problem of some bundled FOML fragments

Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…

Bundled products are often offered as good deals to customers. When we bundle quantifiers and modalities together (as in $\exists x \Box$, $\Diamond \forall x$ etc.) in first-order modal logic (FOML), we get new logical operators whose…

The satisfiability problem for First-order Modal Logic (\FOML) is undecidable even for simple fragments like having only unary predicates, two variables etc. Recently a new way to identify decidable fragments of \FOML has been introduced…

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO$^2$ and the guarded fragment GF. We prove that…

Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $\exists y. \forall x. (\Box_x P(x,y) \supset\Diamond_y P(y,x))$. Like First order…

All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…

We specify the frontier of decidability for fragments of the first-order theory of ordinal multiplication. We give a NEXPTIME lower bound for the complexity of the existential fragment of $\langle \omega^{\omega^\lambda}; \times, \omega,…

While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…

The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…

We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…

We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of…

In this article, we deal with propositional calculi over a signature containing the classical implication $\to$ with the rules of modus ponens and substitution. For these calculi we consider few recognizing problems such as recognizing…

Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and…

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…

We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…

The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…

For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…