Related papers: Recursive Aggregates as Intensional Functions in A…
We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Transformer-based large language models (LLMs) have displayed remarkable creative prowess and emergence capabilities. Existing empirical studies have revealed a strong connection between these LLMs' impressive emergence abilities and their…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Intensional sets, i.e., sets given by a property rather than by enumerating elements, are widely recognized as a key feature to describe complex problems (see, e.g., specification languages such as B and Z). Notwithstanding, very few tools…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
This paper considers the problem of reasoning on massive amounts of (possibly distributed) data. Presently, existing proposals show some limitations: {\em (i)} the quantity of data that can be handled contemporarily is limited, due to the…
The recent explosive interest in the reasoning capabilities of large language models, such as DeepSeek-R1, has demonstrated remarkable success through reinforcement learning-based fine-tuning frameworks, exemplified by methods like Group…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed to model situations where some quantitative strength is associated with arguments. In this setting, the notion of accrual corresponds to sets of arguments that…