Boolean algebras of conditionals, probability and logic

Flaminio, Tommaso; Godo, Lluı́s; Hosni, Hykel

doi:10.1016/j.artint.2020.103347

Cited by 24 publications

(24 citation statements)

References 62 publications

(100 reference statements)

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“…For comparison with other approaches, like [13], see [25,Section 9]. In analogy to formula (2), where the indicator of a conditional event "A given H" is defined as A|H " A ^H `ppA|Hq s H, the iterated conditional "B|K given A|H" is defined as follows (see, e.g., [18,19,22]):…”

Section: Preliminary Notions and Resultsmentioning

confidence: 99%

Interpreting connexive principles in coherence-based probability logic

Pfeifer,

Sanfilippo

2021

Preprint

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We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If ∼A, then A, should not hold, since the conditional's antecedent ∼A contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event A| s A is ppA| s Aq " 0. Moreover, connexive logics aim to capture the intuition that conditionals should express some "connection" between the antecedent and the consequent or, in terms of inferences, validity should require some connection between the premise set and the conclusion. This intuition is covered by a number of principles, a selection of which we analyze in our contribution. We present two approaches to connexivity within coherence-based probability logic. Specifically, we analyze connections between antecedents and consequents firstly, in terms of probabilistic constraints on conditional events (in the sense of defaults, or negated defaults) and secondly, in terms of constraints on compounds of conditionals and iterated conditionals. After developing different notions of negations and notions of validity, we analyze the following connexive principles within both approaches: Aristotle's Theses, Aristotle's Second Thesis, Abelard's First Principle and selected versions of Boethius' Theses. We conclude by remarking that coherence-based probability logic offers a rich language to investigate the validity of various connexive principles.

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Section: Preliminary Notions and Resultsmentioning

confidence: 99%

Interpreting connexive principles in coherence-based probability logic

Pfeifer,

Sanfilippo

2021

Preprint

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“…First, it seems likely that in certain situations, a richer language of conditionals would be useful, eg. considering conditional logics in the style of Kern-Isberner's three-valued conditionals [14] or the logic of Boolean conditionals [6]. Secondly, other interpretations of the probability entailment can be explored: for instance, to allow for interpreting the weights in valued formulas not only as a lower bound but with other constraints like an equality or a strict lower bound, or to compute the probability of the conclusion of an argument by means of the Maximum Entropy distribution underlying the premises [26,22].…”

Section: Future Workmentioning

confidence: 99%

Probabilistic Argumentation: An Approach Based on Conditional Probability –A Preliminary Report–

Dellunde

Godo

Vidal

2021

Lecture Notes in Computer Science

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A basic form of an instantiated argument is as a pair (support, conclusion) standing for a conditional relation 'if support then conclusion'. When this relation is not fully conclusive, a natural choice is to model the argument strength with the conditional probability of the conclusion given the support. In this paper, using a very simple language with conditionals, we explore a framework for probabilistic logic-based argumentation based on an extensive use of conditional probability, where uncertain and possibly inconsistent domain knowledge about a given scenario is represented as a set of defeasible rules quantified with conditional probabilities. We then discuss corresponding notions of attack and defeat relations between arguments, providing a basis for appropriate acceptability semantics, e.g. based on extensions or on DeLP-style dialogical trees.

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“…After obtaining N g , q, q m , u, and u m through the above calculations, equation (22) can calculate an average probability P gq [35] of the generated programs having the pass ratio over 90%, and they are generated from the sample programs. We assume that there are j programs with a pass ratio of code more than 90%, so P(K j |P gt ) represents the probability of the pass ratio of similarity checking more than 90% for these j programs is real, as shown in equation ( 23) [36], where P(K j ∩ P gt ) means the probability of there are at most j programs having the pass ratio of code similarity 10 Scientific Programming checking over 90% in the generated programs, and K j indicates there are j programs having the pass ratio of code similarity checking over 90% within the generated programs produced by the code transform model at a time. According to the abovementioned statistics, we know that the probability of j programs having the pass ratio of code similarity checking over 90% is P(K j |P gt ).…”

Section: Predetermining the Number Of Generated Programsmentioning

confidence: 99%

Applying Code Transform Model to Newly Generated Program for Improving Execution Performance

Chang

Tsai

2021

Scientific Programming

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The existing programs inside the voice assistant machine prompt human-machine interaction in response to a request from a user. However, the crucial problem is that the machine often may not give a proper answer to the user or cannot work out the existing program execution efficiently. Therefore, this study proposes a novel transform method to replace the existing programs (called sample programs in this paper) inside the machine with newly generated programs through code transform model GPT-2 that can reasonably solve the problem mentioned above. In essence, this paper introduces a theoretical estimation in statistics to infer at least a number of generated programs as required so as to guarantee that the best one can be found within them. In addition, the proposed approach not only imitates a voice assistant system with filtering redundant keywords or adding new keywords to complete keyword retrieval in semantic database but also checks code similarity and verifies the conformity of the executive outputs between sample programs and newly generated programs. According to code checking and program output verification, the processes can expedite transform operations efficiently by removing the redundant generated programs and finding the best-performing generated program. As a result, the newly generated programs outperform the sample programs because the proposed approach reduces the number of code lines by 32.71% and lowers the program execution time by 24.34%, which is of great significance.

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Boolean algebras of conditionals, probability and logic

Cited by 24 publications

References 62 publications

Interpreting connexive principles in coherence-based probability logic

Interpreting connexive principles in coherence-based probability logic

Probabilistic Argumentation: An Approach Based on Conditional Probability –A Preliminary Report–

Applying Code Transform Model to Newly Generated Program for Improving Execution Performance

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