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Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
In-context learning (ICL) has proven highly effective across diverse large language model (LLM) tasks. However, its potential for enhancing tasks that demand step-by-step logical deduction, such as mathematical reasoning, remains…
Large language models (LLMs) achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet often generate unnecessarily long reasoning paths that incur high inference cost. Recent self-consistency-based approaches…
Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in LLMs. Interestingly, we observe that both CoT reasoning and self-training share the core objective: iteratively leveraging…
Large language models (LLMs) make remarkable progress in reasoning tasks. Among different reasoning modes, inductive reasoning, due to its better alignment with human learning, attracts increasing interest. However, research on inductive…
This work introduces Symbolic-Aided Chain-of-Thought (CoT), an improved approach to standard CoT, for logical reasoning in large language models (LLMs). The key idea is to integrate lightweight symbolic representations into few-shot…
This paper introduces an explanation framework designed to enhance the quality of rules in knowledge-based reasoning systems based on dataset-driven insights. The traditional method for rule induction from data typically requires…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
We propose a large language model explainability technique for obtaining faithful natural language explanations by grounding the explanations in a reasoning process. When converted to a sequence of tokens, the outputs of the reasoning…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Traditional retrieval methods rely on transforming user queries into vector representations and retrieving documents based on cosine similarity within an embedding space. While efficient and scalable, this approach often fails to handle…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…