Related papers: SROIQsigma is decidable
It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two…
We investigate the expressive power of quantifier alternation hierarchy of first-order logic over words. This hierarchy includes the classes ${\Sigma}_i$ (sentences having at most $i$ blocks of quantifiers starting with an $\exists$) and…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
We introduce the logic $\sf ITL^e$, an intuitionistic temporal logic based on structures $(W,\preccurlyeq,S)$, where $\preccurlyeq$ is used to interpret intuitionistic implication and $S$ is a $\preccurlyeq$-monotone function used to…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Given a Markov decision process (MDP) $M$ and a formula $\Phi$, the strategy synthesis problem asks if there exists a strategy $\sigma$ s.t. the resulting Markov chain $M[\sigma]$ satisfies $\Phi$. This problem is known to be undecidable…
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Extensions of {\omega}-automata to infinite alphabets typically rely on symbolic guards to keep the transition relation finite, and on registers or memory cells to preserve information from past symbols. Symbolic transitions alone are…
We introduce a logic for knowledge representation and reasoning on protein-protein interactions. Modulo a theory, formulas describe protein structures and dynamic changes. They can be composed in order to add or remove static and dynamic…
We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…
Given a $\Pi^{\mu}_2$ formula of the modal $\mu$ calculus, it is decidable whether it is equivalent to a $\Sigma^{\mu}_2$ formula.
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic…
We stratify intuitionistic first-order logic over $(\forall,\to)$ into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We study the decidability and complexity of these…
We present a STIT ('see to it that') logic with discrete temporal operators and deontic operators in which we can formalize and reason about legal concepts such as persistent duty and the dynamic concept of power from Hohfeld. As our main…
It has been an open question as to whether the Modular Structural Operational Semantics framework can express the dynamic semantics of call/cc. This paper shows that it can, and furthermore, demonstrates that it can express the more general…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…