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In the logical framework introduced by Grohe and Tur\'an (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on…
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.
Many satisfiability modulo theories solvers implement a variant of the DPLL(T ) framework which separates theory-specific reasoning from reasoning on the propositional abstraction of the formula. Such solvers conclude that a formula is…
This paper elaborates on a new approach of the question of the proof-theoretic study of concurrent interaction called "proofs as schedules". Observing that proof theory is well suited to the description of confluent systems while…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
We extend the formal framework of classifier models used in the legal domain. While the existing classifier framework characterises cases solely through the facts involved, legal reasoning fundamentally relies on both facts and rules,…
We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its…
We propose a refinement of temporal-difference learning that enforces first-order Bellman consistency: the learned value function is trained to match not only the Bellman targets in value but also their derivatives with respect to states…
A provenance analysis for a query evaluation or a model checking computation extracts information on how its result depends on the atomic facts of the model or database. Traditional work on data provenance was, to a large extent, restricted…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the Algebra of Logic of the 19th century. Schr\"oder investigated it as Aufl\"osungsproblem (solution problem). It is closely related to the modern…
The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite…
Treating diffusion and advection/reaction separately is an effective strategy for solving semilinear advection-diffusion-reaction equations. However, such an approach is prone to suffer from order reduction, especially in the presence of…
Kaplan and Montague have showed that certain intuitive axioms for a first-order theory of knowledge, formalized as a predicate, are jointly inconsistent. Their arguments rely on self-referential formulas. I offer a consistent first-order…