Related papers: Type-elimination-based reasoning for the descripti…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…
This paper presents a proof-theoretic analysis of the modal $\mu$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $\mu$-calculus, using methods from linear logic and its exponential modalities.…
We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
Datalog+/- is a Datalog-based language family enhanced with existential quantification in rule heads, equalities and negative constraints. Query answering over databases with respect to a Datalog+/- theory is generally undecidable, however…
Recent advancements in transformer-based language models have sparked research into their logical reasoning capabilities. Most of the benchmarks used to evaluate these models are simple: generated from short (fragments of) first-order logic…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Differentiable inductive logic programming (ILP) techniques have proven effective at finding approximate rule-based solutions to link prediction and node classification problems on knowledge graphs; however, the common assumption of…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
In the present paper, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The display-approach is suitable to modularly chart the space of dynamic epistemic logics on…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision…
This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying…
Multi-step LLM reasoning over structured tables fails because planning and execution share no explicit cell-grounding contract. Existing methods constrain the planner to a left-to-right factorization at odds with table permutation…
Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such…
Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…
Modern knowledge base systems frequently need to combine a collection of databases in different formats: e.g., relational databases, XML databases, rule bases, ontologies, etc. In the deductive database system DDBASE, we can manage these…