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We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
We present two applications of egglog to mathematical optimization in JijModeling 2, a mathematical modeller whose internal representation is based on simply typed $\lambda$-calculus. First, we use egglog to improve $\LaTeX$ output for…
Under the lens of Marr's levels of analysis, we critique and extend two claims about language models (LMs) and language processing: first, that predicting upcoming linguistic information based on context is central to language processing,…
Over the past few years, the abilities of large language models (LLMs) have received extensive attention, which have performed exceptionally well in complicated scenarios such as logical reasoning and symbolic inference. A significant…
We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit…
Evaluating reasoning ability in Large Language Models (LLMs) is important for advancing artificial intelligence, as it transcends mere linguistic task performance. It involves understanding whether these models truly understand information,…
Integrating large language models (LLMs) with knowledge graphs derived from domain-specific data represents an important advancement towards more powerful and factual reasoning. As these models grow more capable, it is crucial to enable…
Large language models (LLMs) are increasingly used for text analysis tasks, such as named entity recognition or error detection. Unlike encoder-based models, however, generative architectures lack an explicit mechanism to refer to specific…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
Large language models (LLMs) are primarily designed to understand unstructured text. When directly applied to structured formats such as tabular data, they may struggle to discern inherent relationships and overlook critical patterns. While…
Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
The temporal aspect is a significant dimension of our reality. We notice the challenge that large language models (LLMs) face when engaging in temporal reasoning. Our preliminary experiments show that methods involving the generation of…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Type inference is an application domain that is a natural fit for logic programming (LP). LP systems natively support unification, which serves as a basic building block of typical type inference algorithms. In particular, polymorphic type…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…