Related papers: Logic Blog 2023-2024
The goal of this series is to chronicle opinions and issues in the field of machine learning as they stand today and as they change over time. The plan is to host this survey periodically until the AI singularity paperclip-frenzy-driven…
The aim of this paper is to introduce a logic in which nouns and verbs are handled together as a deductive reasoning, and also to observe the relationship between nouns and verbs as well as between logics and conversations.
In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic.
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal…
The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
In the past decade, a lot of progress has been made in the design and evaluation of logic locking; a premier technique to safeguard the integrity of integrated circuits throughout the electronics supply chain. However, the widespread…
This paper presents our system description and error analysis of our entry for NLLP 2024 shared task on Legal Natural Language Inference (L-NLI) \citep{hagag2024legallenssharedtask2024}. The task required classifying these relationships as…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
This paper is an informal survey of some of the deep connections between logic and optimization. It covers George Boole's probability logic, decision diagrams, logic and cutting planes, first order predicate logic, default and nonmonotonic…
These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and…
A group $G$ is called logically cyclic, if it contains an element $s$ such that every element of $G$ can be defined by a first order formula with parameter $s$. The aim of this paper is to investigate the structure of such groups.
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems.