相关论文: OTTER Experiments in a System of Combinatory Logic

Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation…

This paper focuses on the inference of modes for which a logic program is guaranteed to terminate. This generalises traditional termination analysis where an analyser tries to verify termination for a specified mode. Our contribution is a…

We introduce a new type of test, called a Turing Experiment (TE), for evaluating to what extent a given language model, such as GPT models, can simulate different aspects of human behavior. A TE can also reveal consistent distortions in a…

This paper contains examples for a companion paper "The Prolog Debugger and Declarative Programming", which discusses (in)adequacy of the Prolog debugger for declarative programming. Logic programming is a declarative programming paradigm.…

Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…

The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…

We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…

We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a…

Large-scale, pre-trained language models (LMs) have achieved human-level performance on a breadth of language understanding tasks. However, evaluations only based on end task performance shed little light on machines' true ability in…

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and…

This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…

In this paper, we present a mechanism for building hybrid system observers to differentiate between specific positions of the hybrid system. The mechanism is designed through inferring metric temporal logic (MTL) formulae from simulated…

We consider an extension of logic programs, called \omega-programs, that can be used to define predicates over infinite lists. \omega-programs allow us to specify properties of the infinite behavior of reactive systems and, in general,…

OGTT is a common test, frequently used to diagnose insulin resistance or diabetes, in which a patient's blood sugar is measured at various times over the course of a few hours. Recent developments in the study of OGTT results have framed it…

We introduce Euler/X, a toolkit for logic-based taxonomy integration. Given two taxonomies and a set of alignment constraints between them, Euler/X provides tools for detecting, explaining, and reconciling inconsistencies; finding all…

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…

Recent work in explanation generation for decision making agents has looked at how unexplained behavior of autonomous systems can be understood in terms of differences in the model of the system and the human's understanding of the same,…