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Large language models (LLMs) are increasingly used in domains where causal reasoning matters, yet it remains unclear whether their judgments reflect normative causal computation, human-like shortcuts, or brittle pattern matching. We…
In-context learning (ICL) derives its power from enabling Large Language Models to adapt to new tasks via prompt-based reasoning alone, entirely bypassing the need for parameter updates. Existing theories primarily study ICL in single-task…
This paper brings together two lines of research: factor-based models of case-based reasoning (CBR) and the logical specification of classifiers. Logical approaches to classifiers capture the connection between features and outcomes in…
We develop a notion of realizability for Classical Linear Logic based on a concurrent process calculus.
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
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…
Chain-of-thought emerges as a promising technique for eliciting reasoning capabilities from Large Language Models (LLMs). However, it does not always improve task performance or accurately represent reasoning processes, leaving unresolved…
Relational Hoare logics extend the applicability of modular, deductive verification to encompass important 2-run properties including dependency requirements such as confidentiality and program relations such as equivalence or similarity…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…
We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
In-Context Learning (ICL) and Instruction Tuning (IT) are two primary paradigms of adopting Large Language Models (LLMs) to downstream applications. However, they are significantly different. In ICL, a set of demonstrations are provided at…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Our paper investigates the linear logic of knowledge and time LTK_r with reflexive intransitive time relation. The logic is defined semantically, -- as the set of formulas which are true at special frames with intransitive and reflexive…
We found in Homotopy Type Theory (HoTT), a way of representing a first order version of intuitionistic logic (ICL), for intuitionistic calculational logic) where, instead of deduction trees, corresponding linear calculational formats are…
Previous papers give accounts of quests for satisfactory formalizations of the classical informal notion of an algorithm and the contemporary informal notion of an interactive algoritm. In this paper, an attempt is made to generalize the…
In classical logic, "P implies Q" is equivalent to "not-P or Q". It is well known that the equivalence is problematic. Actually, from "P implies Q", "not-P or Q" can be inferred ("Implication-to-Disjunction" is valid), whereas from "not-P…