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Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…

Reading comprehension models have been successfully applied to extractive text answers, but it is unclear how best to generalize these models to abstractive numerical answers. We enable a BERT-based reading comprehension model to perform…

Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially…

This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…

This article looks at how reasoning works in current Large Language Models (LLMs) that function using the token-completion method. It examines their stochastic nature and their similarity to human abductive reasoning. The argument is that…

The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But…

This study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the set-up to be found in modern functional programming languages such as Haskell and ML, although it can…

Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. Define $n$ to be stable if for all $k\ge 0$, we have $\|3^k n\|=\|n\|+3k$. In [7],…

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…

Program text is rendered using impoverished typographic styles. Beyond choice of fonts and syntax-highlighting colors, code editors and related tools utilize very few text decorations. These limited styles are, furthermore, applied in…

Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…

This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…

Recent advancements in Large Language Models (LLMs) have showcased striking results on existing logical reasoning benchmarks, with some models even surpassing human performance. However, the true depth of their competencies and robustness…

In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS…

We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…

Chain-of-Thought (CoT) reasoning has demonstrated remarkable effectiveness in enhancing the reasoning abilities of large language models (LLMs). However, its efficiency remains a challenge due to the generation of excessive intermediate…

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

<Q>_e is the effective list of all finite predicate logic programs. <T_e> is the list of recursive trees. We modify constructions of Marek, Nerode, and Remmel [25] to construct recursive functions f and g such that for all indices e, (i)…