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Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of the article is a proof of the soundness and completeness of CL18 with respect to the semantics of computability logic. [ABSTRACT FROM AUTHOR]

The article delves into the concept of refutation in Gentzen calculi, specifically exploring the differences between intuitionistic and classical logic. It introduces R-formulas and derivability in calculi, emphasizing the need for a semantic foundation to compare various logical systems. The text discusses rules for proving and refuting derivability relations, leading to a deductively closed calculus. It also covers the replacement theorem for Gentzen calculi in the context of K∞, defining logical operators and proving the completeness of the system. The article further examines direct propositional logic in Gentzen calculi, excluding indirect inferences and proving the equivalence of formulas and completeness of operator systems through induction and logical rules. The distinctions between direct logic, intuitionistic logic, and classical propositional logic are discussed within the Gentzen semantics framework, with references to works by Ackermann, Gentzen, Schütte, and von Kutschera. [Extracted from the article]

Strict-Tolerant Logic (ST ) underpins naïve theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical sequent calculus without Cut is sometimes advocated as an appropriate proof-theoretic presentation of ST . Unfortunately, there is only a partial correspondence between its derivability relation and the relation of local metainferential ST -validity – these relations coincide only upon the addition of elimination rules and only within the propositional fragment of the calculus, due to the non-invertibility of the quantifier rules. In this paper, we present two calculi for first-order ST with an eye to recapturing this correspondence in full. The first calculus is close in spirit to the Epsilon calculus. The other calculus includes rules for the discharge of sequent-assumptions; moreover, it is normalisable and admits interpolation. [ABSTRACT FROM AUTHOR]

The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered. [ABSTRACT FROM AUTHOR]

We develop a common semantic framework for the interpretation both of IPC , the intuitionistic propositional calculus, and of logics weaker than IPC (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation. [ABSTRACT FROM AUTHOR]

Abductive reasoning involves finding the missing premise of an "unsaturated" deductive inference, thereby selecting a possible explanans for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as explanans when presented with an abductive problem. Specifically, we show that this set may not include the deductively minimal hypothesis due to the presence of redundant information. We also establish that the set of all analytic hypotheses exhausts all possible solutions to the given problem. Finally, we propose a deductive criterion for differentiating between the best explanans candidates and other hypotheses. [ABSTRACT FROM AUTHOR]

Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL , which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable. [ABSTRACT FROM AUTHOR]

R. Suszko's Sentential Calculus with Identity SCI results from classical propositional calculus CPC by adding a new connective ≡ and axioms for identity φ ≡ ψ (which we interpret here as 'propositional identity'). We reformulate the original semantics of SCI using Boolean prealgebras which, introduced in different ways, are known in the literature as structures for the modeling of (hyper-) intensional semantics. We regard intensionality here as a measure for the discernibility of propositions (and hyperintensionality as a high degree of intensionality). As concrete examples of SCI -based intensional modeling, we review and study algebraic semantics of some Lewis-style modal logics in the vicinity of S 3 and present conditions under which those modal systems can be restored, in a precise sense, as certain axiomatic extensions of SCI . This generalizes work of Suszko which is focused on the modal systems S 4 and S 5 . Our approach is particularly intended as a proposal to consider and to further study SCI (and its extensions) as a general framework for the modeling of (hyper-) intensional semantics. [ABSTRACT FROM AUTHOR]

The main objective of this study is to introduce Sheffer stroke R0-algebra (for short, SR0-algebra). Then it is stated that the axiom system of a Sheffer stroke R0-algebra is independent. It is indicated that every Sheffer stroke R0-algebra is R0-algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R0-algebra are defined, a congruence relation on a Sheffer stroke R0-algebra is determined by the ideal and quotient Sheffer stroke R0-algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R0-algebra constructed by a prime ideal of this algebra is totally ordered and the cardinality is less than or equals to 2. After all, important conclusions are obtained for totally ordered Sheffer stroke R0-algebras by applying various properties of prime ideals. [ABSTRACT FROM AUTHOR]

To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q-Res and QU-Res, and only one specific QBF family to separate Q-Res and QU-Res. Here we provide a general method to construct hard formulas for Q-Res and QU-Res. The construction uses simple propositional formulas (e.g. minimally unsatisfiable formulas) in combination with easy QBF gadgets (Sb 2 formulas without constant winning strategies). This leads to a host of new hard formulas, including new classes of hard random QBFs. We further present generic constructions for formulas separating Q-Res and QU-Res, and for separating Q-Res and LD-Q-Res. [ABSTRACT FROM AUTHOR]

Contingentists—who hold that it is contingent what there is—are divided on the claim that having a property or standing in a relation requires being something. This claim can be formulated as a natural schematic principle of higher-order modal logic. On this formulation, I argue that contingentists who are also higher-order contingentists—and so hold that it is contingent what propositions, properties and relations there are—should reject the claim. Moreover, I argue that given higher-order contingentism, having a property or standing in a relation does not even require possibly being something. [ABSTRACT FROM AUTHOR]

Boolean Dynamical Systems (BDSs) are networks described by Boolean variables. A new representation of BDSs is presented in this article by using modal non-monotonic logic (H ). This approach allows Boolean Networks to be represented by a set of modal formulas and therefore can be used to describe and learn their properties. The study of a BDS focuses in particular on the search of stable configurations, limit cycles and unstable cycles, which help to characterize a large type of Gene Networks. In this article is presented the identification of such asymptotic properties by introduction of a new concept, ghost extensions. Using ghost extensions, it is possible to translate BDSs in propositional calculus and consequently to use SAT algorithms. [ABSTRACT FROM AUTHOR]

Problems of the analysis of natural language texts are considered. In particular, approaches to the partial solution to problems of logical consistency/inconsistency of facts derived from the text, searching for antimems, and constructing ontologies based on the results of the linguistic (semantic-syntactic) analysis of the text are proposed. Logical analysis of the text is performed on the basis of the propositional calculus and methods of proof in this calculus. [ABSTRACT FROM AUTHOR]

Problems of the analysis of natural-language texts are considered. In particular, algorithms for the partial solution of problems of logical consistency/inconsistency of facts derived from the text, search for antimems, and construction of ontologies based on the results of linguistic (semantic-syntactic) analysis of the text are proposed. Logical analysis of the text is performed on the basis of propositional calculus and methods of proof in this calculus. [ABSTRACT FROM AUTHOR]

Copyright of Polish Statistician / Wiadomości Statystyczne is the property of State Treasury - Statistics Poland and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, neuroimaging methods have been used to investigate how the human mind carries out deductive reasoning. According to some, the neural substrate of language is integral to deductive reasoning. According to others, deductive reasoning is supported by a language-independent distributed network including left frontopolar and frontomedial cortices. However, it has been suggested that activity in these frontal regions might instead reflect non-deductive factors such as working memory load and general cognitive difficulty. To address this issue, 20 healthy volunteers participated in an fMRI experiment in which they evaluated matched simple and complex deductive and non-deductive arguments in a 2 × 2 design. The contrast of complex versus simple deductive trials resulted in a pattern of activation closely matching previous work, including frontopolar and frontomedial "core" areas of deduction as well as other "cognitive support" areas in frontoparietal cortices. Conversely, the contrast of complex and simple non-deductive trials resulted in a pattern of activation that does not include any of the aforementioned "core" areas. Direct comparison of the load effect across deductive and non-deductive trials further supports the view that activity in the regions previously interpreted as "core" to deductive reasoning cannot merely reflect non-deductive load, but instead might reflect processes specific to the deductive calculus. Finally, consistent with previous reports, the classical language areas in left inferior frontal gyrus and posterior temporal cortex do not appear to participate in deductive inference beyond their role in encoding stimuli presented in linguistic format.

Background: Null Hypothesis Significance Testing (NHST) has been well criticised over the years yet remains a pillar of statistical inference. Although NHST is well described in terms of statistical models, most textbooks for non-statisticians present the null and alternative hypotheses (H0 and HA, respectively) in terms of differences between groups such as (μ1 = μ2) and (μ1 ≠ μ2) and HA is often stated to be the research hypothesis. Here we use propositional calculus to analyse the internal logic of NHST when couched in this popular terminology. The testable H0 is determined by analysing the scope and limits of the P-value and the test statistic's probability distribution curve. Results: We propose a minimum axiom set NHST in which it is taken as axiomatic that H0 is rejected if P-value< α. Using the common scenario of the comparison of the means of two sample groups as an example, the testable H0 is {(μ1 = μ2) and [( x ¯ 1 ≠ x ¯ 2) due to chance alone]}. The H0 and HA pair should be exhaustive to avoid false dichotomies. This entails that HA is ¬{(μ1 = μ2) and [( x ¯ 1 ≠ x ¯ 2) due to chance alone]}, rather than the research hypothesis (HT). To see the relationship between HA and HT, HA can be rewritten as the disjunction HA: ({(μ1 = μ2) ∧ [( x ¯ 1 ≠ x ¯ 2) not due to chance alone]} ∨ {(μ1 ≠ μ2) ∧ [ (x ¯ 1 ≠ x ¯ 2) not due to (μ1 ≠ μ2) alone]} ∨ {(μ1 ≠ μ2) ∧ [( x ¯ 1≠ x ¯ 2) due to (μ1 ≠ μ2) alone]}). This reveals that HT (the last disjunct in bold) is just one possibility within HA. It is only by adding premises to NHST that HT or other conclusions can be reached. Conclusions: Using this popular terminology for NHST, analysis shows that the definitions of H0 and HA differ from those found in textbooks. In this framework, achieving a statistically significant result only justifies the broad conclusion that the results are not due to chance alone, not that the research hypothesis is true. More transparency is needed concerning the premises added to NHST to rig particular conclusions such as HT. There are also ramifications for the interpretation of Type I and II errors, as well as power, which do not specifically refer to HT as claimed by texts. [ABSTRACT FROM AUTHOR]

Antonio Monteiro gave a characterization of maximal congruences in certain semisimple varieties in order to present a representation theorem for them. Under specific conditions, this theorem can be presented with the same proof for every semisimple variety considered by him. In this note, we show that this notion of maximal congruence is closely linked to Henkin's notion of maximal theories for certain families of logics from the literature of algebraic logic. To see this relation, we study the class of n -valued Hilbert algebras with supremum enriched with Moisil operators. For this class of algebras, we present a sound and complete propositional and first-order calculus. Moreover, we show how this relation works for logics from semisimple varieties studied in the Monteiro's school. Extending the scope of applications, we present soundness and completeness results for some first-order paraconsistent logics through non-deterministic matrix semantics. Despite the fact that these logics are not algebraizable with the Blok-Pigozzi's method, they display an algebraic behaviour that allows us to give a simplified presentation. [ABSTRACT FROM AUTHOR]

In this paper, we prove some important properties on the set SpecμF (L) of all prime μ-filters of an Almost Distributive Lattice(ADL) topo-logically. We established a set of equivalent conditions for SpecμF (L) to become a Hausdorff space. [ABSTRACT FROM AUTHOR]

We study the S5-modal expansion of the Łukasiewicz logic. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respect to this logic. This propositional calculus is then expanded with an infinitary rule to achieve strong completeness. These results are derived from properties of monadic MV-algebras: functional representations of simple and finitely subdirectly irreducible algebras, as well as the finite embeddability property. We also show similar completeness theorems for the extension of the logic based on models with bounded universe. [ABSTRACT FROM AUTHOR]

We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities { □ , ◇ } and its fragments as a formalization for constructively acceptable systems. Calling these calculi constructive , we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including CK , IK , their extensions by the modal axioms T , B , 4, 5, and the axioms for bounded width and depth and their fragments CK □ , propositional lax logic and IPC. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than IPC has a constructive sequent calculus. [ABSTRACT FROM AUTHOR]

Copyright of Aufklärung: Revista de Filosofia is the property of Aufklarung: Revista de Filosofia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Proceedings of the YSU A: Physical & Mathematical Sciences is the property of Publishing House of Yerevan State University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper is a continuation of Inoué [5]. As already mentioned in the paper, a number of intuitionistic provable formulas are given with a Hilbert-style proof. For that, we make use of a family of intuitionistic deduction theorems, which are also presented in this paper by means of Mizar system [2], [1]. Our axiom system of intuitionistic propositional logic IPC is based on the propositional subsystem of H1-IQC in Troelstra and van Dalen [6, p. 68]. We also owe Heyting [4] and van Dalen [7]. Our treatment of a set-theoretic intuitionistic deduction theorem is due to Agata Darmochwał's Mizar article "Calculus of Quantifiers. Deduction Theorem" [3]. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of National Academy of Sciences of Armenia Reports / Doklady Nacionalnaâ Akademiâ Nauk Armenii is the property of National Academy of Sciences of the Republic of Armenia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

t is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natural multiplications extending the one on A. But the essence of A* is completely different. By defining new products, we investigate some algebraic and spectral properties of odd duals of A. We will show relations between these products and Arens products, weak or weak-star continuity, commutativity and unit elements of these algebras. We also determine the spectrum and multiplier algebra for A*, and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras. [ABSTRACT FROM AUTHOR]

The determination of the independence ratio of a periodic net requires finding a subgroup of the translation group of the net for which the quotient graph and a fundamental transversal have the same independence ratio; the respective motif defines a periodic factor of the net. This article deals with practical issues regarding the calculation of the independence ratio of mainly 2‐periodic nets, with an application to the 200 2‐periodic nets listed on the RCSR (Reticular Chemistry Structure Resource) site. A companion paper described a calculation technique of independence ratios of finite graphs based on propositional calculus. This paper focuses on criteria for the choice of the translation subgroup and of the transversal. The translation subgroup should be chosen in such a way as to eliminate every cycle in the quotient graph that is shorter than structural cycles, or rings, of the net. Topological constraints provide an upper bound to the independence ratio of 2‐periodic nets and mostly enable the determination of the associated factor, thus giving a description of a periodic distribution in saturated solid solutions obeying some avoidance rule. [ABSTRACT FROM AUTHOR]

According to comparativism, comparative confidence is more fundamental than absolute confidence. In two recent AJP papers, Stefánsson has argued that comparativism is capable of explaining interpersonal confidence comparisons. In this paper, I will argue that Stefansson's proposed explanation is inadequate; that we have good reasons to think that comparativism cannot handle interpersonal comparisons; and that the best explanation of interpersonal comparisons requires thinking about confidence in a fundamentally different way than that which comparativists propose: specifically, we should think of confidence as a dimensionless quantity. [ABSTRACT FROM AUTHOR]

Let Mm,n be the set of all m-by-n real matrices. A matrix R in Mm,n with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of R is less than 1. For A, B ∈ Mm,n, we say that A is strictly sub row Hadamard majorized by B (denoted by A ...SH B) if there exists an m-by-n strictly sub row stochastic matrix R such that A = R o B where X o Y is the Hadamard product (entrywise product) of matrices X, Y ∈ Mm,n. In this paper, we introduce the concept of strictly sub row Hadamard majorization as a relation on Mm,n. Also, we find the structure of all linear operators T : Mm,n → Mm,n which are preservers (resp. strong preservers) of strictly sub row Hadamard majorization. [ABSTRACT FROM AUTHOR]

An essential point about Stoic philosophy is why certain arguments and rules are basic in their logic. That is the case of the indemonstrables and the themata. It has been proposed that assuming the theory of mental models, one can think that the five indemonstrables and two of the themata are easy to understand for the human mind. This can explain why those arguments and rules are essential components in Stoic logic. In addition, it is relevant because, given that the theory of mental models tries to capture the real way people reason, it can show that Stoic logic is closer to the manner individuals naturally make inferences than modern propositional calculus. The present paper is intended to move forward in this direction. It has two aims: one of them is to give an account from the theory of mental models of all of the themata. The other one is to argue that a simple schema that is correct in modern propositional calculus, and which, however, is not deemed as a true syllogism in Stoic logic, is difficult for people according to the theory of mental models. Those are further pieces of evidence that Stoic logic describes the way human beings think to a greater extent than modern logic. [ABSTRACT FROM AUTHOR]

According to Löwenstein's rule, Al–O–Al bridges are forbidden in the aluminosilicate framework of zeolites. A graph‐theoretical interpretation of the rule, based on the concept of independent sets, was proposed earlier. It was shown that one can apply the vector method to the associated periodic net and define a maximal Al/(Al+Si) ratio for any aluminosilicate framework following the rule; this ratio was called the independence ratio of the net. According to this method, the determination of the independence ratio of a periodic net requires finding a subgroup of the translation group of the net for which the quotient graph and a fundamental transversal have the same independence ratio. This article and a companion paper deal with practical issues regarding the calculation of the independence ratio of mainly 2‐periodic nets and the determination of site distributions realizing this ratio. The first paper describes a calculation technique based on propositional calculus and introduces a multivariate polynomial, called the independence polynomial. This polynomial can be calculated in an automatic way and provides the list of all maximal independent sets of the graph, hence also the value of its independence ratio. Some properties of this polynomial are discussed; the independence polynomials of some simple graphs, such as short paths or cycles, are determined as examples of calculation techniques. The method is also applied to the determination of the independence ratio of the 2‐periodic net dhc. [ABSTRACT FROM AUTHOR]

Uniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as "covers") in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution. [ABSTRACT FROM AUTHOR]

We introduce Mersenne-Lucas hybrid numbers. We give the Binet formula, the generating function, the sum, the character, the norm and the vector representation of these numbers. We find some relations among Mersenne-Lucas hybrid numbers, Jacopsthal hybrid numbers, Jacopsthal-Lucas hybrid numbers and Mersenne hybrid numbers. Then we present some important identities such as Cassini identities for Mersenne-Lucas hybrid numbers. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness. [ABSTRACT FROM AUTHOR]

The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis' account of subject matter. Lewis' proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis' but also includes an attractive characterisation of sentential subject matter. [ABSTRACT FROM AUTHOR]

Yildiz (2016a) proposes a novel tool, namely choice regularities, to classify choice theories according to the syntactic structure of the underlying choice axioms. We focus on the regularity of the SARP-like acyclicity requirements. Axiomatic characterizations of many choice theories contain conditions formulated in the vein of the strong axiom of revealed preference (SARP), such as Masatlioglu et al. (2012)and Yildiz (2016b), in which a binary relation -based on the observed choice behavior- is formulated and its acyclicity is required. We focus on the regularity of the SARP-like acyclicity requirements. For those binary relations that can be represented in a specific form, we find an upper bound on the degree of the free regularities that impose the binary relation to be acyclic. [ABSTRACT FROM AUTHOR]