Related papers: The logic of Turing progressions
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
This work examines the interconnections between logic, epistemology, and sciences within the Naturalist tradition. It presents a scheme that connects logic, mathematics, physics, chemistry, biology, and cognition, emphasizing…
While Chain-of-Thought (CoT) prompting boosts Language Models' (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We…
A resource-bounded version of the statement "no algorithm recognizes all non-halting Turing machines" is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any coNP-complete language and also…
Existential fixed point logic (EFPL) is a natural fit for some applications, and the purpose of this talk is to attract attention to EFPL. The logic is also interesting in its own right as it has attractive properties. One of those…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…
If we assume the Thesis that any classical Turing machine T, which halts on every n-ary sequence of natural numbers as input, determines a PA-provable formula, whose standard interpretation is an n-ary arithmetical relation f(x1, >..., xn)…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. In this kind of scenarios, arising e.g. in knowledge…
Large Language Models (LLMs) are expected to be predictable and trustworthy to support reliable decision-making systems. Yet current LLMs often show inconsistencies in their judgments. In this work, we examine logical preference consistency…
The present work proposes an alternative approach to the problem of the emergence of classicality. Typical approaches developed in the literature derive the classical behaviour of a quantum system from conditions that concern the value of…
The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of…
Semiring provenance is a successful approach to provide detailed information on the combinations of atomic facts that are responsible for the result of a query. In particular, interpretations in general provenance semirings of polynomials…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
The transition from the quantum to the classical world is not yet understood. Here we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except in some specific basis. But we have no…
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor--that of the cascade. The…