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Inductive Logic Programming (ILP) is a form of machine learning (ML) which in contrast to many other state of the art ML methods typically produces highly interpretable and reusable models. However, many ILP systems lack the ability to…
We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The…
We study a sound verification method for parametric component-based systems. The method uses a resource logic, a new formal specification language for distributed systems consisting of a finite yet unbounded number of components. The logic…
Picat, a new member of the logic programming family, follows a different doctrine than Prolog in offering the core logic programming concepts: arrays and maps as built-in data types; implicit pattern matching with explicit unification and…
Chain-of-thought (CoT) reasoning exposes the intermediate thinking process of large language models (LLMs), yet verifying those traces at scale remains unsolved. In response, we introduce the idea of decision pivots-minimal, verifiable…
Mainstream methods for Legal Judgment Prediction (LJP) based on Pre-trained Language Models (PLMs) heavily rely on the statistical correlation between case facts and judgment results. This paradigm lacks explicit modeling of legal…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on 'proof' (as opposed to 'truth'). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Most scientific materials compress reasoning, presenting conclusions while omitting the derivational chains that justify them. This compression hinders verification by lacking explicit, step-wise justifications and inhibits cross-domain…
This paper proposes an integration of temporal logical reasoning and Partially Observable Markov Decision Processes (POMDPs) to achieve interpretable decision-making under uncertainty with macro-actions. Our method leverages a fragment of…
Semiring provenance is a successful approach to provide detailed information on the combinations of atomic facts that are responsible for the result of a query. In particular, interpretations in general provenance semirings of polynomials…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
In this article, we present a leap-forward expansion to the study of explainability in neural networks by considering explanations as answers to abstract reasoning-based questions. With $P$ as the prediction from a neural network, these…
The human reasoning process is seldom a one-way process from an input leading to an output. Instead, it often involves a systematic deduction by ruling out other possible outcomes as a self-checking mechanism. In this paper, we describe the…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
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…
ML4PG is an extension of the Proof General interface, allowing the user to invoke machine-learning algorithms and find proof similarities in Coq/SSReect libraries. In this paper, we present three new improvements to ML4PG. First, a new…
Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the…