Related papers: Exploring Non-Regular Extensions of Propositional …

We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…

We introduce a description logic ALCQIO_{b,Re} which adds reachability assertions to ALCQIO, a sub-logic of the two-variable fragment of first order logic with counting quantifiers. ALCQIO_{b,Re} is well-suited for applications in software…

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…

This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…

Reinforcement learning (RL) faces challenges in evaluating policy trajectories within intricate game tasks due to the difficulty in designing comprehensive and precise reward functions. This inherent difficulty curtails the broader…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two…

In the last 20 years many proposals have been made to incorporate non-monotonic reasoning into description logics, ranging from approaches based on default logic and circumscription to those based on preferential semantics. In particular,…

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in…

In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational…

Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…

Vision Language Navigation (VLN) requires agents to follow natural language instructions by grounding them in sequential visual observations over long horizons. Explicit reasoning could enhance temporal consistency and perception action…

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…

This paper proposes a connection method \`a la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL $\mathcal{ALCH}$ extended with two typicality operators: one on (complex) concepts and…

Hyperproperties are a modern specification paradigm that extends trace properties to express properties of sets of traces. Temporal logics for hyperproperties studied in the literature, including HyperLTL, assume a synchronous semantics and…

The paper studies problems of satisfiability, decidability and admissibility of inference rules, conceptions of knowledge and agent's knowledge in non-transitive temporal linear logic LTL(Past,m). We find algorithms solving mentioned…

Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…

Diffusion Large Language Models (dLLMs) are rapidly emerging alongside autoregressive models as a powerful paradigm for complex reasoning, with reinforcement learning increasingly used for downstream alignment. Existing trajectory-based RL…

We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a semiring structure. PL is designed for complex quantitative…