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.

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)

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 cannot possibly reach its own line 06 and halt 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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)

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)

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.

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)

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 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.

This study used a partial least squares structural equation modelling (PLS-SEM) to estimate curriculum management's direct and indirect effects on university graduate programmes' viability. The study also examined the role of institutional effectiveness in mediating the nexus between the predictor and response variables. This is a correlational study with a factorial research design. The study's participants comprised 149 higher education administrators (23 Faculty Deans and 126 HODs) from two public universities in Nigeria. A structured questionnaire designed by the researchers was (...) used for data collection. The questionnaire was duly validated with an acceptable scale and item content validity indices. The dimensionality of the instrument was determined using exploratory factor analysis (EFA). Convergent validity was based on Average Variance Extracted (AVE), whereas discriminant validity was based on Fornell-Lacker criteria and the Hetero-Trait Mono-Trait (HTMT) ratio. Acceptable composite reliability estimates of internal consistency were reached for the three sub-scales. Following ethical practices, the questionnaire was physically administered to respondents and retrieved afterwards. Smart PLS (version 3.2.9) and SPSS (version 26.0) programs were used for all the statistical analyses. This study uncovered significant direct and indirect effects of curriculum management on the viability of graduate programmes. Institutional effectiveness significantly impacted graduate programmes’ viability while mediating the nexus between curriculum management and graduate programmes’ viability. Curriculum management and institutional effectiveness jointly explained a significant proportion of graduate programmes’ viability variance. The result of this study proved that graduate programmes’ viability depends, to a great extent, on how much curriculum is managed and how effective institutions are with their services. The result of this study can enable institutions seeking to run viable graduate programmes to re-evaluate their curriculum management practices and the effectiveness of their services. (shrink)

Logic has a fundamental role in the philosophy of Franjo Marković (1845-1914). His theory of concepts and reasoning is analyzed, especially with respect to the essential role of the principle of sufficient reason and in connection with the concept of causality. The interplay of various types of evidence in Marković's inductive-deductive logic is analysed by means of contemporary justification logic tools.

Purpose: This study investigates the interrelationship among COVID-19 anxiety, mindfulness, COVID-19 information avoidance, preventive behavior, and academic performance. Research methodology: The study assessed protective factors as mediators of COVID-19 anxiety and academic performance using WarpPLS. The study participants were K-12 Filipino students from a secondary school in Cagayan, Philippines, identified through convenience sampling. Results: COVID-19 anxiety, mindfulness, information avoidance, and preventive behavior were found to be negatively correlated. Preventive behavior is associated with improved academic performance. Conversely, there was a negative (...) correlation between mindfulness, COVID-19 information avoidance, and academic performance. The association between COVID-19 anxiety and academic achievement is only mediated by mindfulness and preventive behavior. Limitations: Preventive factors that may affect COVID-19 anxiety and academic achievement are only considered. Also, the participants are limited to a secondary school in Cagayan, Philippines. Contribution: With the pandemic having a substantial influence on the municipality, the study would be helpful to manage and control the effect of the outbreak on the academic performance of the learners. (shrink)

Although this concept already existed that for the notion of punishments the term Hadd (pl.Hudood) is very feebly defined in Islamic Law. But to point out a deficiency in anything is much easier than to tell why this deficiency occurs and how should it be overcome? According to the beliefs of Abrahamic religions, God is the King of this world and it is agreed principle of English as well as Arabic language that words of King always considered correct and pure (...) and always prevail over the words of a layman. In this research on the basis of opinions of Islamic scholars and in the light of the verses of Quraan i.e words of God, it has been proved that existing concept of the term Hadd (pl.Hudood) is not based on the words of King of this world i.e God but on the words of human being and the term Hadd (pl.Hudood) should not be used as any connection with punishments in Islamic Criminal Law because the King of this world didn't reveal the term Hadd (pl.Hudood) in any sense of punishments like whipping, stoning to death and amputation. The next question arises that if this idea is correct then in which sense the King of this world revealed the term Hadd (pl.Hudood) in Quraan? That's why in the next step an attempt has been made as to what could be possible definition of the term Hadd (pl.Hudood) if this term is to be used in Islamic Law and it was found that in the words of King of this world the term Hadd (pl.Hudood) should not be used in Criminal Law but in Civil Law. The derived definition has been termed as Quraanic definition of Hadd (pl.Hudood). (shrink)

Previous research has interlinked alcohol consumption (AC), mental stress (MS), psychotic experiences (PE), and academic performance (AP) of students and psychological behavior of the general population. The current study seems to be the first to consider the joint and partial mediation effects of MS and PE in linking AC to graduates’ job performance in specific areas such as teamwork (TW), communication competence (CC), customer service (CS), and job functions (JF). A virtual cross-section of 3,862 graduates with self-reported cases of having (...) taken alcohol in the past participated in the study. These participants responded to an electronic questionnaire that was mailed to them. The instrument used for data collection had acceptable psychometric properties. The study used the partial least squares structural equation modeling (PLS-SEM) to achieve its objectives. The inner and outer models were all evaluated for quality and goodness of fit. Results showed a significant negative effect of AC and MS on graduates’ job performance in terms of TW, CC, CS, and JF, respectively. AC had a significant positive effect on MS and PE. MS had a significant positive effect on PE. A significant joint mediation effect of MS and PE was found in linking AC to graduates’ TW, CC, and CS, excluding JF. MS partially mediated AC’s paths to all the graduates’ job performance indicators. PE was only a significant partial mediator of the connection between AC to JF, but not TW, CC, and CS. This study’s result can help improve graduates’ work effectiveness and has revealed some negative predictors. Therefore, it is recommended that graduates avoid alcohol or only consume mild quantities of it to enable them to discharge services effectively at the workplace. (shrink)

Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames.

Public Libraries (PLs) continue to contribute a great deal to user education in local communities. This paper analyzes the importance of PLs in driving community literacy through promotion of user education for the progressive improvement of the society. The paper stresses the relevance and value of PLs by reassessing the benefits they accrue by analyzing the impact of PLs on community and social education. As indigenous knowledge repositories, PLs play a significant role as community information service providers by driving community (...) literacy. The goal of this paper is to analyze the role played by PLs in driving community education and promoting information literacy in the society. PLs, being storehouses of knowledge, support user education by undertaking active part in community information services. The model helps in explaining and analyzing the efficiency of information search and retrieval process in PLs and how it affects user education and community literacy. The paper also discusses the relevance and value of PLs in this age of digital technology. The findings reinforce the claim that PLs are relevant even in this digital age, and they indeed support user education for the progressive improvement of the society. (shrink)

As sustainable tourism gains increasing attention, understanding the factors that influence travelers' motivation to engage with sustainable travel agents becomes crucial. This study investigates the moderating effect of social media usage on the relationship between the perceived value of websites and motivational factors for sustainable travel agents. The study proposes that social media usage acts as a moderator in shaping the relationship between the perceived value of websites and motivational factors. This study has utilized smart tourism. Therefore, independent variable motivation (...) in terms of informativeness gratification and gratification acted as moderating variables. This study has utilized an online questionnaire adapted from a standardized questionnaire based on the literature review. Moreover, a total of 146 managers were surveyed in which they were required to respond to 55 items that elicited the 7 variables social media use, Propensity, perceived website value, motivating factors, entertainment gratification, informativeness gratification, sustainable smart tourism. The data were analyzed by SPSS and PLS-SEM. The findings indicated that relevance and importance of social media use and sustainable smart tourism. The result revealed that 7 hypotheses had a significant relationship. 3 hypotheses did not show a moderating effect. Overall, this study extends the understanding of sustainable smart tourism. These findings will benefit travel agents’ managers in Malaysia to better understand the role of social media use and utilize it towards developing sustainable sustainable smart tourism. (shrink)

The concept of adaptation is employed in many fields such as biology, psychology, cognitive sciences, robotics, social sciences, even literacy and art,1 and its meaning varies quite evidently according to the particular research context in which it is applied. We expect to find a particularly rich catalogue of meanings within evolutionary biology, where adaptation has held a particularly central role since Darwin’s The Origin of Species (1859) throughout important epistemological shifts and scientific findings that enriched and diversified the concept. Accordingly, (...) a conceptual taxonomy of adaptation in evolutionary biology may help to disambiguate it. Interdisciplinary researches focused on adaptation would benefit from such a result. In the present work we recognize and define seven different meanings of adaptation: (1) individual fitness; (2) adaptation of a population; (3) adaptation as the process of natural selection; (4) adaptive traits; (5) molecular adaptation; (6) adaptation as structural tinkering; (7) plasticity. For convenience here, we refer to them as W-, P-, NS-, T-, M-, S- and PL-ADAPTATION. We present the seven meanings in some detail, hinting at their respective origins and conceptual developments in the history of evolutionary thought (references are offered for further deepening). However, it is important to point out that evolution researchers seldom if ever refer to a single meaning purified from the others. This applies also to the authors we cite as representatives of one of the seven meanings. In Discussion and Conclusion draw from our work some future perspectives for adaptation within evolutionary biology. (shrink)

The global pandemic of COVID 19 has changed consumer behaviour to reduce the risk. This is common for all interpersonal interactions of individuals especially in maintaining the recommended interpersonal distance based on the recommendations from the health experts. Sri Lanka as a developing country affected by COVID 19, observed changes in individuals' day today’ consumption decision making due to pandemic. Importantly the retailing sector is highly influenced by the conditions since the frequency of interpersonal interactions and degree of interaction is (...) higher in the retailing sector. Interestingly the retailing sector with its largest contributor, the SMEs need to identify the unique changes that happen to the consumer behaviour in responding to them. Accordingly, the objective of the study is to examine the impact of infectious disease risk on the perceived retail crowding in two perspectives of human density and the spatial density. The study has used a quantitative survey in collecting data with the online self-administrated questionnaire with a sample of 100 consumers. Data analysis has been done by using a PLS-SEM with the support of SmartPLS version 3. The key findings of the study emphasize the significant positive influence of infectious disease risk on human density as well as on the spatial density. Based on the findings the study attempts to provide the implications for the retailing industry to cope with situational changes in the environment. (shrink)