Related papers: PIE -- Proving, Interpolating and Eliminating on t…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…
Intensional sets, i.e., sets given by a property rather than by enumerating elements, are widely recognized as a key feature to describe complex problems (see, e.g., specification languages such as B and Z). Notwithstanding, very few tools…
Despite large language models (LLMs) have achieved remarkable success, their prefix-only prompting paradigm and sequential generation process offer limited flexibility for bidirectional information. Diffusion large language models (dLLMs)…
It has been shown that the existence of a Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) simplifies many numerical aspects of analysis, simulation, and optimal control. However, the PIE…
With rise of digital age, there is an explosion of information in the form of news, articles, social media, and so on. Much of this data lies in unstructured form and manually managing and effectively making use of it is tedious, boring and…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
Learning template based information extraction from documents is a crucial yet difficult task. Prior template-based IE approaches assume foreknowledge of the domain templates; however, real-world IE do not have pre-defined schemas and it is…
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…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
Emerging large language model (LLM) applications involve diverse reasoning strategies and agentic workflows, straining the capabilities of existing serving systems built on a monolithic token generation loop. This paper introduces Pie, a…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Finding the most probable (MAP) model in SRL frameworks such as Markov logic and Problog can, in principle, be solved by encoding the problem as a `grounded-out' mixed integer program (MIP). However, useful first-order structure disappears…
Prompt optimization automatically refines prompting expressions, unlocking the full potential of LLMs in downstream tasks. However, current prompt optimization methods are costly to train and lack sufficient interpretability. This paper…
We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems…
Traditionally, in Programming-by-example (PBE) the goal is to synthesize a program from a small set of input-output examples. Lately, PBE has gained traction as a few-shot reasoning benchmark, relaxing the requirement to produce a program…