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Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
Proof assistants offer tactics to facilitate inductive proofs. However, it still requires human ingenuity to decide what arguments to pass to those induction tactics. To automate this process, we present smart_induct for Isabelle/HOL. Given…
Issues of safety, explainability, and efficiency are of increasing concern in learning systems deployed with hard and soft constraints. Symbolic Constrained Learning and Knowledge Distillation techniques have shown promising results in this…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Deep learning models are widely used for various industrial and scientific applications. Even though these models have achieved considerable success in recent years, there exists a lack of understanding of the rationale behind decisions…
Realizability interprets propositions as specifications for computational entities in programming languages. Specifically, syntactic realizability is a powerful machinery that handles realizability as a syntactic translation of propositions…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
Closed-source large language models (LLMs), such as ChatGPT and Gemini, are increasingly consulted for medical advice, yet their explanations may appear plausible while failing to reflect the model's underlying reasoning process. This gap…