A pair of C functions are defined such that D has the halting problem proof's pathological relationship to simulating termination analyzer H. When H correctly determines that D correctly simulated by H must be aborted to prevent its own infinite execution then H is necessarily correct to reject D as specifying non-halting behavior. This exact same reasoning is applied to the Peter Linz Turing machine based halting problem proof. ...

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.

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 sound arguments are derived from truth preserving finite string transformations applied to true premises.

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.

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] having true premises and now we have [deductively sound formal proofs of mathematical logic].

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 conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

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 incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...) only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete. (shrink)

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 conclusions are the result of these finite string transformation rules.

We begin with the hypothetical assumption that Tarski’s 1933 formula ∀ True(x) φ(x) has been defined such that ∀x Tarski:True(x) ↔ Boolean-True. On the basis of this logical premise we formalize the Truth Teller Paradox: "This sentence is true." showing syntactically how self-reference paradox is semantically ungrounded.

Hehner and Stoddart agree that the halting problem has an inconsistent, unsatisfiable specification. Hehner and Macias agree that a key issue with the halting problem is that it requires a: subjective specification(Hehner) / context dependent function(Macias). When a problem has an unsatisfiable specification because this specification is inconsistent then the unsatisfiability of the specification is anchored in its error thus does not actually limit computation.

A simulating halt decider correctly predicts whether or not its correctly simulated input can possibly reach its own final state and halt. It does this by correctly recognizing several non-halting behavior patterns in a finite number of steps of correct simulation. Inputs that do terminate are simply simulated until they complete.

A simulating halt decider correctly predicts what the behavior of its input would be if this simulated input never had its simulation aborted. It does this by correctly recognizing several non-halting behavior patterns in a finite number of steps of correct simulation. -/- When simulating halt decider H correctly predicts that directly executed D(D) would remain stuck in recursive simulation (run forever) unless H aborts its simulation of D this directly applies to the halting theorem.

The novel concept of a simulating halt decider enables halt decider H to to correctly determine the halt status of the conventional “impossible” input D that does the opposite of whatever H decides. This works equally well for Turing machines and “C” functions. The algorithm is demonstrated using “C” functions because all of the details can be shown at this high level of abstraction.

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 mode until after it determines that its input will never reach its final state. This eliminates the conventional feedback loop where the behavior of the halt decider effects the behavior of its input.

MIT Professor Michael Sipser has agreed that the following verbatim paragraph is correct (he has not agreed to anything else in this paper) -------> -/- If simulating halt decider H correctly simulates its input D until H correctly determines that its simulated D would never stop running unless aborted then H can abort its simulation of D and correctly report that D specifies a non-halting sequence of configurations.

The novel concept of a simulating halt decider enables halt decider H to to correctly determine the halt status of the conventional “impossible” input D that does the opposite of whatever H decides. This works equally well for Turing machines and “C” functions. The algorithm is demonstrated using “C” functions because all of the details can be shown at this high level of abstraction. ---------------------------------------------------------------------------------------------------- ---- Simulating halt decider H correctly determines that D correctly simulated by H would remain stuck in (...) recursive simulation never reaching its own final state. D cannot do the opposite of the return value from H because this return value is unreachable by every correctly simulated D. This same result is shown to be derived in the Peter Linz Turing machine based proof. (shrink)

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 operating system (based on an excellent open source x86 emulator) was created to study the details of the halting problem proof counter-examples at the much higher level (...) of abstraction of C/x86. (shrink)

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.

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 decidability.

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.

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 showing that Tarski's assumptions were wrong.

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 initial state to final states corresponding the mathematical logic functions of Halts(Wm, W) or Loops(Wm, W), halting undecidability has been (...) decided. (shrink)

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). -- .

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 translates into x86 and what an x86 process emulator is. No knowledge of the halting problem is required.

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 and reject expressions that evaluate to neither True nor False.

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 three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.

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 from formal systems is transforming the formal proofs of symbolic logic to use the sound deductive inference model.

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 behavior when it is simulated by the UTM contained within its simulating halt decider while this (...) SHD remains in UTM mode. (shrink)

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.

When we understand that every potential halt decider must derive a formal mathematical proof from its inputs to its final states previously undiscovered semantic details emerge. -/- When-so-ever the potential halt decider cannot derive a formal proof from its input strings to its final states of Halts or Loops, undecidability has been decided. -/- The formal proof involves tracing the sequence of state transitions of the input TMD as syntactic logical consequence inference steps in the formal language of Turing Machine (...) Descriptions. (shrink)

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. Syntax is provided to enable quantifiers to specify type. FOL is a subset of MTT. The ASSIGN_ALIAS operator := enables FOL expressions to be chained together to form HOL expressions.

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.

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 shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...) never sentences of any formal logic system. (shrink)

When we look at 800,000 year ice core data CO2 levels since 1950 have risen at a rate of 123-fold faster than the fastest rate in 800,000 years. When we see that this rise 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 correlation between CO2 and global temperatures seems to be predicting at least 9 degrees C of more warming based on current CO2 levels.

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 True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be (...) semantically incorrect. (shrink)

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 deductive conclusions without any need for other representations.

The fail-safe makes sure the fee is high enough to meet carbon emission reduction targets. The safeguard keeps the fee from getting any higher than needed. -/- One of the ways that we could account for the unpredictability of the price elasticity of demand for carbon would be to provide a fail-safe mechanism to ensure that we definitely stay on the carbon reduction schedule. If we keep Energy Innovation Act (HR 763) essentially as it is and scale up the annual (...) carbon fee increase by Number-of-Years-Behind-Schedule * 0.15. (shrink)

The generalized conclusion of the Tarski and Gödel proofs: All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences. Is not the immutable truth that Tarski made it out to be it is only based on his starting assumptions. -/- When we reexamine these starting assumptions from the perspective of the philosophy of logic we find that there are alternative ways that formal systems can be defined that make undecidability inexpressible in all of these formal systems.

One of the ways that we could account for the unpredictability of the price elasticity of demand for carbon would be to provide a fail-safe mechanism to ensure that we definitely stay on the carbon reduction schedule. If we kept Energy Innovation Act (HR 763) essentially as it is and scale up the annual carbon fee increase by Number-of-Years-Behind-Schedule * 0.15.

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.

This article aims to read feminist new materialisms (Barad), together with ‘postulated’ linguistic or cultural primacy of Queer Theory (Butler), to show how both are engaged in similar critical-ethical endeavours. The central argument is that the criticism of Barad and new materialisms misses Butler’s materialistic insights due to a narrow interpretation of Butler's alleged social-constructivist position. There is, therefore, a specific focus on where they both make similar ethical appeals. Moreover, the article relies on Adorno's negative dialectic to highlight an (...) interpretation of Barad and Butler as being part of the same dialectical movement, in which materialism and idealism fluctuate in their mutual criticisms, thus continuing the procession towards 'new knowledge' and emancipation, or freedom, through their motions back and forth. (shrink)

Pekakak adalah salah satu tokoh yang memiliki pengetahuan mendalam dan perencanaan yang cermat. Saat fajar menyingsing, ia terlihat bertengger di atas pohon. Dengan kemampuan sempurna untuk mengontrol kecepatan penerbangan miliknya, seperti kapan harus memperlambat atau mempercepat, dia dapat dengan mudah menghitung cara optimal untuk menangkap ikan.

The Upanishads reveal that in the beginning, nothing existed: “This was but non-existence in the beginning. That became existence. That became ready to be manifest”. (Chandogya Upanishad 3.15.1) The creation began from this state of non-existence or nonduality, a state comparable to (0). One can add any number of zeros to (0), but there will be nothing except a big (0) because (0) is a neutral number. If we take (0) as Nirguna Brahman (God without any form and attributes), then (...) from where and how did the universe come into existence? -/- The neutral power (0) cannot produce anything without having an element of duality in it. Although Nirguna Brahman is neutral, it has a positive, negative, and neutral pole, constituting its Prakriti or nature. Prakriti has three latent Gunas (modes or qualities): Satva, Rajas, and Tamas. They are related to Gyana Shakti (the power of knowledge) Sankalpa Shakti (the power of ideation), and Kriya Shakti (the power of action). Science says that Atom is the basic element from which the universe evolved. The Atom has three nuclei- electron, pluton, and neutron. The Satva, Rajas, and Tamas in Indian spirituality are nothing but the mystical names for the nuclei of an atom. -/- According to Bhagavata Purana, Prakriti is also constituted of the elements of Time, Karma (action/destiny) and Swabhava (innate nature). Time disturbs the equilibrium of Gunas. From the aspect of Karma is produced an entity called Mahat, in the form of intelligence. Mahat is dominated by Satva and Rajas. From Mahat manifests the next evolute dominated by Tamas with three predominant qualities – Dravya (substance), Kriya (action), as well as intelligence. It forms to become the Ego principle (Ahamkara). -/- Ahamkara has three modes – Satvic, Rajasic and Tamasic. Satvic is Jnana oriented, Rajasic action-oriented and Tamasic Dravya (substance) oriented. From the Tamasic Ahankara, five gross elements are produced (ether, air, fire, water, and earth - Akash, Vayu, Agni, Jal and Prithvi). From the Satvic Ahamkara, guardian deities (the sun and moon, deities of sense organs, and organs of action) and from Rajasic Ahamkara, ten senses (Indriyas), five senses of perception, five organs of action, the faculties of intellect and Prana (life breath) are produced. -/- Bhagavata says that since these energies, elements, and faculties remained disassociated, they were combined to form a Cosmic Egg. The egg floats in the primal waters for a thousand years. Then God enters this Cosmic Egg and manifests himself as the Cosmic Purusha. He is the first nucleus, the God particle equivalent to the number (1) which is the embodiment of everything in the universe. The concept of creation and dissolution in Hinduism can be compared to the waves in an ocean that appear and disappear incessantly. The Manvantaras are such successive episodes of creation emerging from the Cosmic Person, the Manu who is embodied God-Consciousness, God himself. These episodes of creation are measured in Hinduism in terms of Manvantaras, the epochs of Manus. -/- Manu is the ‘First-Born’ (1) of God, the Cosmic Purusha from whom the world has originated. This Cosmic Person (Purusha) has been described as having fourteen biospheres (heavens) that are inhabited by various life forms in the order of evolution of consciousness. If we begin from the human biosphere (Bhuloka), there are ten astral biospheres that a man must transcend to attain liberation or Mukti from the cycle of births and deaths. -/- The number (1) produces the primary numbers up to (9) through the transmutation of the creational energies and qualities. The process can be related to the descent and cyclical evolution of (1) through ten spiritual stages, finally merging with the nondual (0). The number (10) marks the merger of (1) with (0). The Hindu worldview is that all life forms in an episode of creation must evolve to become one with the non-dual state (0) to attain liberation from the cycle of births and deaths in a cyclical process. -/- . (shrink)

How does microbiota research impact our understanding of biological individuality? We summarize the interdisciplinary summer school on "Microbiota, Symbiosis and Individuality: Conceptual and Philosophical Issues" (July 2019), which was supported by a European Research Council starting grant project "Immunity, DEvelopment, and the Microbiota" (IDEM). The summer school centered around interdisciplinary group work on four facets of microbiota research: holobionts, individuality, causation, and human health. The conceptual discussion of cutting-edge empirical research provided new insights into microbiota and highlights the value of (...) incorporating into meetings experts from other disciplines, such as philosophy and history of science. (shrink)

To demarcate the limits of experimental knowledge, we probe the limits of what might be called an experiment. By appeal to examples of scientific practice from astrophysics and analogue gravity, we demonstrate that the reliability of knowledge regarding certain phenomena gained from an experiment is not circumscribed by the manipulability or accessibility of the target phenomena. Rather, the limits of experimental knowledge are set by the extent to which strategies for what we call ‘inductive triangulation’ are available: that is, the (...) validation of the mode of inductive reasoning involved in the source-target inference via appeal to one or more distinct and independent modes of inductive reasoning. When such strategies are able to partially mitigate reasonable doubt, we can take a theory regarding the phenomena to be well supported by experiment. When such strategies are able to fully mitigate reasonable doubt, we can take a theory regarding the phenomena to be established by experiment. There are good reasons to expect the next generation of analogue experiments to provide genuine knowledge of unmanipulable and inaccessible phenomena such that the relevant theories can be understood as well supported. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’. (shrink)

A lineage of prominent philosophers who have discussed the second-person relation can be regarded as advancing structural accounts. They posit that the second-person relation effects one transformative change to the structure of practical reasoning. In this paper, I criticise this orthodoxy and offer an alternative, substantive account. That is, I argue that entering into second-personal relations with others does indeed affect one's practical reasoning, but it does this not by altering the structure of one's agential thought, but by changing what (...) reasons can become available. The importance of second-personal thought for action is heterogenous. Second-person relations make possible the emergence of a wide variety of different kinds of practical reasons: creating some, revealing others. Recognising this diminishes the appeal of the traditional, structural accounts of the practical significance of such second-personal relations. Moving away from structural accounts facilitates a more thorough understanding of the intersubjective form of action. (shrink)

On-line, just as off-line, there are ways of assessing the credibility of information sources. The Internet, although it arguably makes for nothing wholly new in this regard, complicates the ordinary task of assessing credibility. In the first section, I consider a specific example and argue that Internet content providers have no clear interest in resolving these comlications. In the second, I consider four general ways that we might assess credibility and explore how they apply to life online. Finally, I argue (...) that even careful information gathering may pose subtle pitfalls but that some of these may be mitigated on-line. (shrink)

Data access control is a challenging issue in public cloud storage systems. Ciphertext-Policy Attribute-Based Encryption (CP-ABE) has been adopted as a promising technique to provide flexible, fine-grained and secure data access control for cloud storage with honest-but- curious cloud servers. However, in the existing CP-ABE schemes, the single attribute authority must execute the time-consuming user legitimacy verification and secret key distribution, and hence it results in a single-point performance bottleneck when a CP-ABE scheme is adopted in a large-scale cloud storage (...) system. Users may be stuck in the waiting queue for a long period to obtain their secret keys, thereby resulting in low-efficiency of the system. Although multi authority access control schemes have been proposed, these schemes still cannot overcome the drawbacks of single-point bottleneck and low efficiency, due to the fact that each of the authorities still independently manages a disjoint attribute set. In this paper we propose a system that improves the approach of CP-ABE from text based asymmetric to Image based symmetric approach for faster encryption as well as access to data. We also propose a multiple access policy generation for single user where we will be able to implement one to many and many to many methodology. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent (...) scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)