EARLY STRUCTURAL REASONING. GENTZEN 1932

2015 ◽  
Vol 8 (4) ◽  
pp. 662-679 ◽  
Author(s):  
ENRICO MORICONI
Keyword(s):  
Inference Rules ◽  
Structural Reasoning ◽  
Opening Section

AbstractThis paper is a study of the opening section of Gentzen’s first publication of 1932, Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen, a text which shows the relevance of Hertz’s work of the 1920’s for the young Gentzen. In fact, Gentzen borrowed from Hertz the analysis of the notion of consequence, which was given in terms of the rules of thinning (Verdünnung) and cut (Schnitt) on sequents (there called “sentences”(Sätze)). Moreover, following Hertz again, he also judged it necessary to justify the forms of inference of the system by providing a semantics for them, so that it became possible to make precise the informal notion of consequence, and to show that the inference rules adopted are correct and sufficient.

Explanatory Power for Medical Expert Systems: Studies in the Representation of Causal Relationships for Clinical Consultations

1982 ◽  
Vol 21 (03) ◽  
pp. 127-136 ◽  
Author(s):  
J. W. Wallis ◽  
E. H. Shortliffe
Keyword(s):  
Explanatory Power ◽  
Prototype System ◽  
Inference Rules ◽  
Medical Expert ◽  
Comprehensive Knowledge ◽  
Different Types ◽  
Medical Expert Systems ◽  
Explanation System ◽  
Systems Studies

This paper reports on experiments designed to identify and implement mechanisms for enhancing the explanation capabilities of reasoning programs for medical consultation. The goals of an explanation system are discussed, as is the additional knowledge needed to meet these goals in a medical domain. We have focussed on the generation of explanations that are appropriate for different types of system users. This task requires a knowledge of what is complex and what is important; it is further strengthened by a classification of the associations or causal mechanisms inherent in the inference rules. A causal representation can also be used to aid in refining a comprehensive knowledge base so that the reasoning and explanations are more adequate. We describe a prototype system which reasons from causal inference rules and generates explanations that are appropriate for the user.

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

Algorithmic Logic with Recursive Functions

1981 ◽  
Vol 4 (4) ◽  
pp. 975-995
Author(s):  
Andrzej Szałas
Keyword(s):  
Completeness Theorem ◽  
Inference Rules ◽  
Partial Correctness ◽  
Recursive Functions ◽  
Algorithmic Logic ◽  
Block Structured

A language is considered in which the reader can express such properties of block-structured programs with recursive functions as correctness and partial correctness. The semantics of this language is fully described by a set of schemes of axioms and inference rules. The completeness theorem and the soundness theorem for this axiomatization are proved.

Inference rules using local contexts

1988 ◽  
Vol 4 (4) ◽  
pp. 445-462 ◽  
Author(s):  
Leonard G. Monk
Keyword(s):  
Inference Rules ◽  
Local Contexts

Ontological Knowledge Representation and Inference Rules for MTM Decision Support System

2014 ◽  
Author(s):  
Rahul Renu ◽  
Gregory Mocko
Keyword(s):  
Decision Support ◽  
Decision Support System ◽  
Knowledge Representation ◽  
Support System ◽  
Time Estimation ◽  
Time Measurement ◽  
Inference Rules ◽  
Assembly Time ◽  
Time Estimates ◽  
Definition Of

The objective of the research presented is to develop and implement an ontological knowledge representation for Methods-Time Measurement assembly time estimation process. The knowledge representation is used to drive a decision support system that provides the user with intelligent MTM table suggestions based on assembly work instructions. Inference rules are used to map work instructions to MTM tables. An explicit definition of the assembly time estimation domain is required. The contribution of this research, in addition to the decision support system, is an extensible knowledge representation that models work instructions, MTM tables and mapping rules between the two which will enable the establishment of assembly time estimates. Further, the ontology provides an extensible knowledge representation framework for linking time studies and assembly processes.

אצחצח דבר גבורות: The Discovery of the Opening Section of Shelomo Suleiman al-Sinjari’s Seder ha-ʿAvodah

Zutot ◽  
2021 ◽  
pp. 1-7
Author(s):  
Eden Menachem Hacohen
Keyword(s):  
Critical Edition ◽  
Correct Identification ◽  
Research Project ◽  
Hebrew Poetry ◽  
Cairo Geniza ◽  
Opening Section

Abstract This is the first publication of the beginning of one of the sidrei ʿavodah for the Day of Atonement by Shelomo Suleiman al-Sinjari, a prolific Palestinian paytan who lived in the second half of the 9th century. Although well known to researchers, this piyyut was incorrectly attributed to the greatest Palestinian poet: Eleazar b. Qallir. My consultation of a copy of the seder ʿavodah in a Cairo Geniza manuscript and the database of the Ezra Fleischer Geniza Research Project for Hebrew Poetry led to the correct identification of the author of אצחצח דבר גבורות as Shelomo Suleiman. The article contains a critical edition of the beginning of this seder ʿavodah with annotations and variants.

Singular Terms, Identity, and the Creation of Fictional Characters

Disputatio ◽  
2019 ◽  
Vol 11 (54) ◽  
pp. 207-229
Author(s):  
Matthieu Fontaine
Keyword(s):  
Original Work ◽  
Proper Names ◽  
Fictional Characters ◽  
Inference Rules ◽  
Singular Terms ◽  
The Creation ◽  
Abstract Artifacts

Abstract How to interpret singular terms in fiction? In this paper, we address this semantic question from the perspective of the Artifactual Theory of Fiction (ATF). According to the ATF, fictional characters exist as abstract artifacts created by their author, and preserved through the existence of copies of an original work and a competent readership. We pretend that a well-suited semantics for the ATF can be defined with respect to a modal framework by means of Hintikka’s world lines semantics. The question of the interpretation of proper names is asked in relation to two inference rules, problematic when applied in intensional contexts: the Substitution of Identicals and Existential Generalization. The former fails because identity is contingent. The latter because proper names are not necessarily linked to well-identified individuals. This motivates a non-rigid interpretation of proper names in fiction, although cross-fictional reference (e.g. to real entities) is made possible by the interpretative efforts of the reader.

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