Related papers: Nominal Matching Logic
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
The field of machine learning (ML) is concerned with the question of how to construct algorithms that automatically improve with experience. In recent years many successful ML applications have been developed, such as datamining programs,…
We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…
Recent work in machine learning increasingly attributes human-like capabilities such as reasoning or theory of mind to large language models (LLMs) on the basis of benchmark performance. This paper examines this practice through the lens of…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Deep learning (DL) based language models achieve high performance on various benchmarks for Natural Language Inference (NLI). And at this time, symbolic approaches to NLI are receiving less attention. Both approaches (symbolic and DL) have…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Normative reasoning is a type of reasoning that involves normative or deontic modality, such as obligation and permission. While large language models (LLMs) have demonstrated remarkable performance across various reasoning tasks, their…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
We present Probabilistic Decision Model and Notation (pDMN), a probabilistic extension of Decision Model and Notation (DMN). DMN is a modeling notation for deterministic decision logic, which intends to be user-friendly and low in…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML needs a well-defined, fully explored semantics. Such semantics is required in order to…