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The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Structured prediction models aim at solving a type of problem where the output is a complex structure, rather than a single variable. Performing knowledge distillation for such models is not trivial due to their exponentially large output…
System and software design benefits greatly from formal modeling, allowing for automated analysis and verification early in the design phase. Current methods excel at checking information flow and component interactions, ensuring…
We introduce an abductive method for a coherent integration of independent data-sources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…
Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
This paper develops a comprehensive framework for artificial intelligence systems that operate under strict epistemic constraints, moving beyond stochastic language prediction to support structured reasoning, propositional commitment, and…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…
Recent advancements in image synthesis are fueled by the advent of large-scale diffusion models. Yet, integrating realistic object visualizations seamlessly into new or existing backgrounds without extensive training remains a challenge.…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…