Related papers: A strong intuitionistic theory of functionals
Structured, procedural reasoning is essential for Large Language Models (LLMs), especially in mathematics. While post-training methods have improved LLM performance, they still fall short in capturing deep procedural logic on complex tasks.…
In this paper we investigate using the methodology of algebraic logic, deep algebraic results to prove three new omitting types theorems for finite variable fragments of first order logic. As a sample, we show that it T is an L_n theory and…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
Large language models (LLMs) are often portrayed as merely imitating linguistic patterns without genuine understanding. We argue that recent findings in mechanistic interpretability (MI), the emerging field probing the inner workings of…
Computational modelling offers a powerful tool for formalising psychological theories, making them more transparent, testable, and applicable in digital contexts. Yet, the question often remains: how should one computationally model a…
The paper is a first of two and aims to show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive…
Logic programming (LP) is a programming language based on first-order Horn clause logic that uses SLD-resolution as a semi-decision procedure. Finite SLD-computations are inductively sound and complete with respect to least Herbrand models…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
In this paper, we introduce a novel team semantics of LTL inspired by inquisitive logic. The main features of the resulting logic, we call InqLTL, are the intuitionistic interpretation of implication and the Boolean semantics of…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer…
The BERT model has arisen as a popular state-of-the-art machine learning model in the recent years that is able to cope with multiple NLP tasks such as supervised text classification without human supervision. Its flexibility to cope with…
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
Recent years have seen the rise of large language models (LLMs), where practitioners use task-specific prompts; this was shown to be effective for a variety of tasks. However, when applied to semantic textual similarity (STS) and natural…
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…