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To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
The emergence of long-context large language models (LLMs) has enabled the use of hundreds, or even thousands, of demonstrations for in-context learning (ICL) - a previously impractical regime. This paper investigates whether traditional…
This paper introduces the first, open source software library for Constraint Consistent Learning (CCL). It implements a family of data-driven methods that are capable of (i) learning state-independent and -dependent constraints, (ii)…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
In-context learning (ICL) has emerged as a successful paradigm for leveraging large language models (LLMs). However, it often struggles to generalize beyond the distribution of the provided demonstrations. A recent advancement in enhancing…
Large language models~(LLMs) exhibit exceptional performance in language tasks, yet their auto-regressive inference is limited due to high computational requirements and is sub-optimal due to the exposure bias. Inspired by speculative…
Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…
We introduce iterative retrieval, a novel framework that empowers retrievers to make iterative decisions through policy optimization. Finding an optimal portfolio of retrieved items is a combinatorial optimization problem, generally…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more…
Effective organization of in-context learning (ICL) demonstrations is key to improving the quality of large language model (LLM) responses. To create better sample-label pairs that instruct LLM understanding, we introduce logit…
Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of…
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…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…