# PL OlcottPixels2Words

PL Olcott

BSBA 1986 and equivalent of BS in Computer Science

## About

37

Publications

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Introduction

Created the x86utm operating system to concretely examine the halting problem in the high level language of C. Partial halt decider H examines the behavior of a simplified version of the Peter Linz Ĥ by simulating Ĥ in its x86 emulator.
H decides that the computation Ĥ(Ĥ) specifies infinitely nested simulation that must be aborted. This same reasoning is applied to the actual Peter Linz proof deriving the same conclusion: H(Ĥ, Ĥ) is decided as non-halting.

## Publications

Publications (37)

This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into thre...

This is an explanation of a possible new insight into the halting problem provided in the language of software engineering. Technical computer science terms are explained using software engineering terms. No knowledge of the halting problem is required.
It is based on fully operational software executed in the x86utm operating system. The x86utm...

This is an explanation of a key new insight into the halting problem provided in the language of software engineering. Technical computer science terms are explained using software engineering terms.
To fully understand this paper a software engineer must be an expert in the C programming language, the x86 programming language, exactly how C tran...

A Simulating Halt Decider (SHD) computes the mapping from its input to its own accept or reject state based on whether or not the input simulated by a UTM would reach its final state in a finite number of simulated steps.
A halt decider (because it is a decider) must report on the behavior specified by its finite string input. This is its actual...

By making a slight refinement to the halt status criterion measure that remains consistent with the original a halt decider may be defined that correctly determines the halt status of the conventional halting problem proof counter-examples. This refinement overcomes the pathological self-reference issue that previously prevented halting decidabilit...

The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.

The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. The pathological self-reference of the conventional halting problem proof counter-examples is overcome. The halt status of these examples is correctly determined. A simulating halt decider remains in pure simulation mod...

This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system).

An abstract machine having a tape head that can be advanced in 0 to 0x7FFFFFFF increments an unlimited number of times specifies a model of computation that has access to unlimited memory. The technical name for memory addressing based on displacement from the current memory address is relative addressing.

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is...

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings.
Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive c...

The huge spike in atmospheric CO2 from 300 ppm to 413 ppm has no other possible cause besides human activity. The only reason that the Earth is hundreds of degrees hotter than the Moon (at night) is the greenhouse effect of Earth's atmosphere. Combining these two basic facts proves beyond doubt that human CO2 emissions are causing the Earth to heat...

None of the pending legislation or projections of emission reduction impacts of carbon fees realistically examine plausible values for the price elasticity of demand for gasoline. To drop gasoline consumption by 50% requires much higher carbon fees than are currently being considered. When 29% of CO2 emissions come from the transportation sector dr...

Since 1950 CO2 has been increasing at least 100 times faster and has risen 32% greater than in the prior 800,000 years. C02 is currently higher than it has been in 15 million years.
The recent CO2 increase was directly measured by instruments and the 800,000 year old values were directly measured from air bubbles trapped in columns of ice.

When we look at 800,000 year ice core data CO2 levels since 1950 have sharply spiked at a rate 11,400% than the fastest rate in 800,000 years. When we see that this huge spike in CO2 is precisely correlated with global carbon emissions the human link to climate change seems certain and any rebuttal becomes ridiculously implausible. The 800,000 year...

A sufficiently steep carbon fee ensuring carbon reduction targets are definitely met on schedule along with a corresponding carbon dividend minimizing the transition burden to the public. The dividend would aim for the average person to break-even throughout the whole transition process. The fail-safe makes sure the fee is high enough to meet carbo...

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of s...

Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]?
All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] h...

Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model.
Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusi...

Tarski "proved" that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language.
The only thing required to eliminate incompleteness, undecidability and inconsistency fro...

If the conclusion of the Tarski Undefinability Theorem was that some artificially constrained limited notions of a formal system necessarily have undecidable sentences, then Tarski made no mistake within his assumptions. When we expand the scope of his investigation to other notions of formal systems we reach an entirely different conclusion showin...

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations such as model theory.

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations such as model theory.

Formal specification of Minimal Type Theory (essentially Higher Order Logic with types).
This is the formal YACC BNF specification for Minimal Type Theory (MTT). MTT was created by augmenting the syntax of First Order Logic (FOL) to specify Higher Order Logic (HOL) expressions using FOL syntax

Within the (Haskell Curry) notion of a formal system we complete Tarski's formal correctness: ∀x True(x) ↔ ⊢ x and use this finally formalized notion of Truth to refute his own Undefinability Theorem (based on the Liar Paradox), the Liar Paradox, and the (Panu Raatikainen) essence of the conclusion of the 1931 Incompleteness Theorem.

For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts.
By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize a...

For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts.

If there truly is a proof that shows that no universal halt decider exists on the basis that certain tuples: (H, Wm, W) are undecidable, then this very same proof (implemented as a Turing machine) could be used by H to reject some of its inputs. When-so-ever the hypothetical halt decider cannot derive a formal proof from its input strings and initi...

By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of...

Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax.
The increase in expressiveness over other formal systems of logic...

Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.

This paper derives mathematical mapping theory of truth on the basis of the Alfred Tarski semantic conception of truth. It accomplishes this by reverse engineering previously unknown details of the Tarski theory via a specific concrete example. This example shows the atomic semantic meaning of φ(x) in the following Tarski formula: For all x, True(x...

Hypothesis:
WFF(x) can be applied syntactically to the semantics of formalized declarative sentences such that: WFF(x) ↔ (x ↦ True) ∨ (x ↦ False) (see proof sketch below) For clarity we focus on simple propositions without binary logical connectives.

(1) Every TM / input pair either halts or fails to halt.
(2) There exists a TM halt decider for every TM / input pair.
(3) A SMTM can become any element of the set of TMs.
(4) Therefore a SMTM can become a halt decider for any TM input pair.

A method and system for recognizing machine generated character glyphs in a graphic image that uses a deterministic finite automaton (DFA) to separately recognize the individual pixelcolumns of character glyphs and then combines these separate pixelcolumns together to form correctly recognized whole glyphs. This method and system can enable data to...

A deterministic finite automaton uses binary search (and optionally hashing) method(s) of sparse matrix representation to recognize the graphical representations of characters or icons from a bitmap representation of the computer screen. This recognition can be applied to translate data from an unknown form of original specification (file format) i...

## Questions

Question (1)

Halting problem undecidability and infinitely nested simulation

## Projects

Projects (2)