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The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
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…
LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
We now have a wide range of proof assistants available for compositional reasoning in monoidal or higher categories which are free on some generating signature. However, none of these allow us to represent categorical operations such as…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…
Neural networks (NNs) are pervasive across various domains but often lack interpretability. To address the growing need for explanations, logic-based approaches have been proposed to explain predictions made by NNs, offering correctness…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent…
Multi-adjoint logic programming is a general framework with interesting features, which involves other positive logic programming frameworks such as monotonic and residuated logic programming, generalized annotated logic programs, fuzzy…
We prove that if two linear codes are equivalent then they are semi-linearly equivalent. We also prove that if two additive MDS codes over a field are equivalent then they are additively equivalent.
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
Machine reading comprehension has aroused wide concerns, since it explores the potential of model for text understanding. To further equip the machine with the reasoning capability, the challenging task of logical reasoning is proposed.…
Table-based fact verification task aims to verify whether the given statement is supported by the given semi-structured table. Symbolic reasoning with logical operations plays a crucial role in this task. Existing methods leverage programs…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
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)…
How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…