102,077 research outputs found
On the Foundations of Computing: Limits and Open Issues
No full textAny attempt to conceptualize, categorize and constraint foundational issues in a living science, such as Computing, is bound to show its limitations and leave a number of open issues. Taking stock with some critical reviews of Primiero (On the foundations of computing, Oxford University Press, Oxford, 2019) published in this Journal, I overview potential new problems to be investigated by a foundational analysis of the science of computing
An epistemic logic for becoming informed
No full textVarious conceptual approaches to the notion of information can currently be traced in the literature in logic and formal epistemology. A main issue of disagreement is the attribution of truthfulness to informational data, the so called Veridicality Thesis (Floridi 2005). The notion of Epistemic Constructive Information (Primiero 2007) is one of those rejecting VT. The present paper develops a formal framework for ECI. It extends on the basic approach of Artemov's logic of proofs (Artemov 1994), representing an epistemic logic based on dependent justifications, where the definition of information relies on a strict distinction from factual truth. The definition obtained by comparison with a Normal Modal Logic translates a constructive logic for "becoming informed": its distinction from the logic of "being informed"aEuro"which internalizes truthfulness-is essential to a general evaluation of information with respect to truth. The formal disentanglement of these two logics, and the description of the modal version of the former as a weaker embedding into the latter, allows for a proper understanding of the Veridicality Thesis with respect to epistemic states defined in terms of information
Epistemic Modalities
No full textI present an analysis of the notion of epistemic modalities, based on an appropriate interpretation of two basic constructivist issues: verification and epistemic agency. Starting from an historical analysis of conditions for judgments, I analyze first the reading of necessity with respect to apodictic judgements, and then that of possibility with respect to hypothetical judgement. The analysis results in a formal treatment of rules for judgemental modal operators, whose aim is to preserve epistemic states corresponding to verified and unverified assumptions in contexts. In the conclusion, further tracks of research are indicated for designing a semantic framework and defining multi-agents systems
Type-theoretical dynamics: exploring belief revision in a constructive framework
No full textIn the present paper a dynamics for type theory is introduced. The formalization provides epistemic explanations for the basic notions of belief state and belief set by referring to assertion conditions for type-theoretical judgements; it interprets expectations in terms of default assumptions for such a structure and it adapts the usual revision operations and the analogous of the Ramsey test. The model, restricted to operations of revision, merging and information preference, provides a constructive type-theoretical approach to epistemic dynamics
Proof-checking Bias in Labeling Methods
No full textWe introduce a typed natural deduction system designed to formally verify the presence of bias in automatic labeling methods. The system relies on a ”data-as-terms” and ”labels-as-types” interpretation of formulae, with derivability contexts encoding probability distributions on training data. Bias is understood as the divergence that expected probabilistic labeling by a classifier trained on opaque data displays from the fairness constraints set by a transparent dataset
A possible worlds semantics for trustworthy non-deterministic computations
No full textThe notion of trustworthiness, central to many fields of human inquiry, has recently attracted the attention of various researchers in logic, computer science, and artificial intelligence (AI). Both conceptual and formal approaches for modeling trustworthiness as a (desirable) property of AI systems are emerging in the literature. To develop logics fit for this aim means to analyze both the non-deterministic aspect of AI systems and to offer a formalization of the intended meaning of their trustworthiness. In this work we take a semantic perspective on representing such processes, and provide a measure on possible worlds for evaluating them as trustworthy. In particular, we intend trustworthiness as the correspondence within acceptable limits between a model in which the theoretical probability of a process to produce a given output is expressed and a model in which the frequency of showing such output as established during a relevant number of tests is measured. From a technical perspective, we show that our semantics characterizes the probabilistic typed natural deduction calculus introduced in D'Asaro and Primiero (2021)[12] and further extended in D'Asaro et al. (2023) [13]. This contribution connects those results on trustworthy probabilistic processes with the mainstream method in modal logic, thereby facilitating the understanding of this field of research for a larger audience of logicians, as well as setting the stage for an epistemic logic appropriate to the task
Offline and online data: on upgrading functional information to knowledge
No full textThis paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories
A taxonomy of errors for information systems
No full textWe provide a full characterization of computational error states for information systems. The class of errors considered is general enough to include human rational processes, logical reasoning, scientific progress and data processing in some functional programming languages. The aim is to reach a full taxonomy of error states by analysing the recovery and processing of data. We conclude by presenting machine-readable checking and resolve algorithms
Algorithmic Iteration for Computational Intelligence
No full textMachine awareness is a disputed research topic, in some circles considered a crucial step in realising Artificial General Intelligence. Understanding what that is, under which conditions such feature could arise and how it can be controlled is still a matter of speculation. A more concrete object of theoretical analysis is algorithmic iteration for computational intelligence, intended as the theoretical and practical ability of algorithms to design other algorithms for actions aimed at solving well-specified tasks. We know this ability is already shown by current AIs, and understanding its limits is an essential step in qualifying claims about machine awareness and Super-AI. We propose a formal translation of algorithmic iteration in a fragment of modal logic, formulate principles of transparency and faithfulness across human and machine intelligence, and consider the relevance to theoretical research on (Super)-AI as well as the practical import of our results
An epistemic constructive definition of information
No full textThe present paper formulates an Epistemic Constructive Definition of Information (ECDI), based on the rejection of the alethic nature ascribed to declarative objective semantic information (DOS). ECDI reformulates the principles holding for the non-alethic Standard Definition of Information (SDI), it is based on the Verificationist Principle of Truth and it refers to the typical constructive distinction between judgemental act and propositional content. The resulting framework defines two distinct and complementary epistemic acts: justifications and conditions of knowledge. Finally, the concept of information is formally presented within the syntactic-semantic method of Constructive Type Theory (CTT)
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