Related papers: Notes on applicative matching logic
Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures of robustness and generalization. This paper attributes these deficiencies to spurious reasoning, i.e.,…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
We wish to present a mirrored language structure (MLS) and four logic rules determined by this structure for the model of a computable Oracle Turing machine. MLS has novel features that are of considerable biological and computational…
Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule we call sequential product that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL).…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…
We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers with the goal of learning mathematical functions from data. LGML consists of two phases, namely a…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Argument mining (AM) is the process of automatically extracting arguments, their components and/or relations amongst arguments and components from text. As the number of platforms supporting online debate increases, the need for AM becomes…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Recent advances in Large Language Models (LLMs) have raised interest in their formal reasoning capabilities, particularly in mathematics. While closed LLMs like GPT-4 perform well on mathematical benchmarks, e.g., GSM8K, it remains unclear…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic…
LLMs trained in the understanding of programming syntax are now providing effective assistance to developers and are being used in programming education such as in generation of coding problem examples or providing code explanations. A key…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…