Related papers: Layered Fixed Point Logic
Despite recent advances in training and prompting strategies for Large Language Models (LLMs), these models continue to face challenges with complex logical reasoning tasks that involve long reasoning chains. In this work, we explore the…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
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…
We study a mutually enriching connection between response time analysis in real-time systems and the mixing set problem. Thereby generalizing over known results we present a new approach to the computation of response times in…
Runtime analysis aims at contributing to our understanding of evolutionary algorithms through mathematical analyses of their runtimes. In the context of discrete optimization problems, runtime analysis classically studies the time needed to…
Natural language is among the most accessible tools for explaining decisions to humans, and large pretrained language models (PLMs) have demonstrated impressive abilities to generate coherent natural language explanations (NLE). The…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…
As the application of deep neural networks proliferates in numerous areas such as medical imaging, video surveillance, and self driving cars, the need for explaining the decisions of these models has become a hot research topic, both at the…
We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic…
Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is…
We develop a novel analytical method for studying optimal paths in dynamic optimization problems under general monotonicity conditions. The method centers on a locator function -- a simple object constructed directly from the model's…
In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and…
Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…