Related papers: Non-commutative linear logic fragments with sub-co…
This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…
While large models achieve impressive results, their learning dynamics are far from understood. Many domains of interest, such as natural language syntax, coding languages, arithmetic problems, are captured by context-free grammars (CFGs).…
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)}…
We study the algorithmic properties of first-order monomodal logics of frames $\langle \mathbb{N}, \leq \rangle$, $\langle \mathbb{N}, < \rangle$, $\langle \mathbb{Q}, \leq \rangle$, $\langle \mathbb{Q}, < \rangle$, $\langle \mathbb{R},…
We introduce and develop propositional continuous intuitionistic logic and propositional continuous affine logic via complete algebraic semantics. Our approach centres on AC-algebras, which are algebras $USC(\mathcal{L})$ of sup-preserving…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of…
Let $A_N$ denote nondeterministic automatic complexity and \[ L_{k,c}=\{x\in [k]^* : A_N(x)> |x|/c\}. \] In particular, $L_{k,2}$ is the language of all $k$-ary words for which $A_N$ is maximal, while $L_{k,3}$ gives a rough dividing line…
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…
Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As…
Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…
Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any…
Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…
We study nonlinear connectives (exponentials) in the context of Type Logical Grammar (TLG). We devise four conservative extensions of the displacement calculus with brackets, DbC, DbCM, DbCb and DbCbMr which contain the universal and…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
Large language models are often assumed to acquire increasingly structured, generalizable internal representations simply by scaling data and parameters. We interrogate this assumption by introducing a Clinical Trial Natural Language…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…