Related papers: MSO+nabla is undecidable
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…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
The goal of this paper is to establish that it remains undecidable whether a sequent is provable in two systems in which a weakening rule for an exponential modality is completely omitted from classical propositional linear logic…
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that the…
We address questions of logic and expressibility in the context of random rooted trees. Infiniteness of a rooted tree is not expressible as a first order sentence, but is expressible as an existential monadic second order sentence (EMSO).…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We study the problem of enumerating the answers to a query formulated in monadic second order logic (MSO) over an unranked forest F that is compressed by a straight-line program (SLP) D. Our main result states that this can be done after…
In logics for the strategic reasoning the main challenge is represented by their verification in contexts of imperfect information and perfect recall. In this work, we show a technique to approximate the verification of Alternating-time…
We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs.
The reachability problem in multi-pushdown automata (MPDA) has many applications in static analysis of recursive programs. An example is safety verification of multi-threaded recursive programs with shared memory. Since these problems are…
The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known…
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…
We establish the decidability of the $\Sigma_2$ theory of both the arithmetic and hyperarithmetic degrees in the language of uppersemilattices i.e. the language with $\leq, 0$ and $\sqcup$. This is achieved by using Kumabe-Slaman forcing -…
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set,…