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003 OCoLC;

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006 m o d ;

007 cr unu||||||||;

008 230609s2023 ncua obm 000 0 eng d;

035 a| (OCoLC)1381680658;

090 a| QA9.45;

049 a| EREE;

100 1 a| Crumpler, Charles,e| author.?| UNAUTHORIZED;

245 10 a| Inferences over fields :b| a preliminary investigation into the deductive capabilities of field-theoretically defined logical connectives /c| by Charles Crumpler.;

246 3 a| Inferences over fields a preliminary investigation into the deductive capabilities of field-theoretically defined logical connectives;

264 1 a| [Greenville, N.C.] :b| [East Carolina University],c| 2023.;

300 a| 1 online resource (49 pages) :b| illustrations;

336 a| textb| txt2| rdacontent;

337 a| computerb| c2| rdamedia;

338 a| online resourceb| cr2| rdacarrier;

347 a| text fileb| PDFc| 360.9 KB2| rda;

538 a| System requirements: Adobe Reader.;

538 a| Mode of access: World Wide Web.;

502 b| M.A.c| East Carolina Universityd| 2023.;

500 a| Presented to the Faculty of the Department of Mathematics;

500 a| Advisor: Zachary Robinson;

500 a| Title from PDF t.p. (viewed August 27, 2024).;

520 3 a| In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic 2. We begin by discussing the historical context in which this research occurs. In subsequent sections, we will construct the field, called F₄ and describing the algebraic structure over F₄. We then define the connectives [wedge], [vee], and [negation] over F₄ by extending their standard definition over F₂. We define the basic syntax and semantics of F₄. We show that [wedge] and [vee] are dual over F₄ with respect to [negation] and that F₄ is functionally complete over {[wedge], [vee], [negation] } [union] F₄. We develop a notion of inferences over F₄ by imbuing it with a partial order, defining validity and the material implication, and defining a proof. Upon completing this, we prove the Deduction, Soundness, and Completeness Theorems, thereby showing that inferences over F₄ behaves in ways comparable to, but not equivalent to, those over a field of two values in characteristic 2.;

504 a| Includes bibliographical references.;

650 0 a| Many-valued logic.=| ^A68468;

650 0 a| Completeness theorem.=| ^A94327;

653 a| logic;

653 a| soundness;

700 1 a| Robinson, Zachary,e| degree supervisor.1| https://id.oclc.org/worldcat/entity/E39PCjCcxbQJqMkGdq3yJtd9tC=| ^A465635;

710 2 a| East Carolina University.b| Department of Mathematics.?| UNAUTHORIZED;

856 40 z| Access via ScholarShipu| http://hdl.handle.net/10342/12853;

994 a| C0b| ERE;

596 a| 1 4;

998 a| 6143757;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6143757-1001l| JNETm| JOYNERr| Ys| Yt| JNE3ETDu| 6/9/2023x| ETDz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6143757-2001l| HSLELECm| HSLr| Ys| Yt| HEETDu| 6/9/2023x| ETDz| HERESOURCE;

Inferences over fields : a preliminary investigation into the deductive capabilities of field-theoretically defined logical connectives / by Charles Crumpler.

Author/creator	Crumpler, Charles author.
Other author	Robinson, Zachary, degree supervisor.
Other author	East Carolina University. Department of Mathematics.
Format	Theses and dissertations
Publication	[Greenville, N.C.] : [East Carolina University], 2023.
Description	1 online resource (49 pages) : illustrations
Supplemental Content	Access via ScholarShip
Subjects	Many-valued logic. Completeness theorem.

Variant title	Inferences over fields a preliminary investigation into the deductive capabilities of field-theoretically defined logical connectives
Summary	In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic 2. We begin by discussing the historical context in which this research occurs. In subsequent sections, we will construct the field, called F₄ and describing the algebraic structure over F₄. We then define the connectives [wedge], [vee], and [negation] over F₄ by extending their standard definition over F₂. We define the basic syntax and semantics of F₄. We show that [wedge] and [vee] are dual over F₄ with respect to [negation] and that F₄ is functionally complete over {[wedge], [vee], [negation] } [union] F₄. We develop a notion of inferences over F₄ by imbuing it with a partial order, defining validity and the material implication, and defining a proof. Upon completing this, we prove the Deduction, Soundness, and Completeness Theorems, thereby showing that inferences over F₄ behaves in ways comparable to, but not equivalent to, those over a field of two values in characteristic 2.
General note	Presented to the Faculty of the Department of Mathematics
General note	Advisor: Zachary Robinson
General note	Title from PDF t.p. (viewed August 27, 2024).
Dissertation note	M.A. East Carolina University 2023.
Bibliography note	Includes bibliographical references.
Technical details	System requirements: Adobe Reader.
Technical details	Mode of access: World Wide Web.

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