Journal articles on the topic 'Logic'
To see the other types of publications on this topic, follow the link: Logic.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 journal articles for your research on the topic 'Logic.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.
1
Holba, Jiří. "Buddhismus a aristotelská logika." FILOSOFIE DNES 3, no. 1 (June 17, 2011): 27–36. http://dx.doi.org/10.26806/fd.v3i1.60.
Full textAbstract:
Abstrakt/Abstract Článek pojednává o buddhistické logice a jejím vztahu k logice aristotelské, zejména k principu sporu a principu vyloučeného třetího. Dotkne se také dialetheismu a parakonzistentních logik, které se v souvislosti s interpretacemi buddhismu objevují. The article deals with the Buddhist logic and its relation to Aristotle’s logic, in particular, to the principle of non-contradiction and the principle of exluded middle. It also tackles the topic of dialetheism and paraconsistent logics, which are sometimes mentioned in connection with the interpretations of Buddhism.
2
Holba, Jiří. "Buddhismus a aristotelská logika." FILOSOFIE DNES 3, no. 1 (June 17, 2011): 27–36. http://dx.doi.org/10.26806/fd.v3i1.325.
Full textAbstract:
Abstrakt/Abstract Článek pojednává o buddhistické logice a jejím vztahu k logice aristotelské, zejména k principu sporu a principu vyloučeného třetího. Dotkne se také dialetheismu a parakonzistentních logik, které se v souvislosti s interpretacemi buddhismu objevují. The article deals with the Buddhist logic and its relation to Aristotle’s logic, in particular, to the principle of non-contradiction and the principle of exluded middle. It also tackles the topic of dialetheism and paraconsistent logics, which are sometimes mentioned in connection with the interpretations of Buddhism.
3
Lewitzka, Steffen. "Abstract Logics, Logic Maps, and Logic Homomorphisms." Logica Universalis 1, no. 2 (August 8, 2007): 243–76. http://dx.doi.org/10.1007/s11787-007-0013-z.
Full text
4
Oliveira, Kleidson Êglicio Carvalho da Silva. "Paraconsistent Logic Programming in Three and Four-Valued Logics." Bulletin of Symbolic Logic 28, no. 2 (June 2022): 260. http://dx.doi.org/10.1017/bsl.2021.34.
Full textAbstract:
AbstractFrom the interaction among areas such as Computer Science, Formal Logic, and Automated Deduction arises an important new subject called Logic Programming. This has been used continuously in the theoretical study and practical applications in various fields of Artificial Intelligence. After the emergence of a wide variety of non-classical logics and the understanding of the limitations presented by first-order classical logic, it became necessary to consider logic programming based on other types of reasoning in addition to classical reasoning. A type of reasoning that has been well studied is the paraconsistent, that is, the reasoning that tolerates contradictions. However, although there are many paraconsistent logics with different types of semantics, their application to logic programming is more delicate than it first appears, requiring an in-depth study of what can or cannot be transferred directly from classical first-order logic to other types of logic.Based on studies of Tarcisio Rodrigues on the foundations of Paraconsistent Logic Programming (2010) for some Logics of Formal Inconsistency (LFIs), this thesis intends to resume the research of Rodrigues and place it in the specific context of LFIs with three- and four-valued semantics. This kind of logics are interesting from the computational point of view, as presented by Luiz Silvestrini in his Ph.D. thesis entitled “A new approach to the concept of quase-truth” (2011), and by Marcelo Coniglio and Martín Figallo in the article “Hilbert-style presentations of two logics associated to tetravalent modal algebras” [Studia Logica (2012)]. Based on original techniques, this study aims to define well-founded systems of paraconsistent logic programming based on well-known logics, in contrast to the ad hoc approaches to this question found in the literature.Abstract prepared by Kleidson Êglicio Carvalho da Silva Oliveira.E-mail: kecso10@yahoo.com.brURL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/322632
5
Tulenheimo, Tero. "Three Nordic Neo-Aristotelians and the First Doorkeeper of Logic." Studia Neoaristotelica 19, no. 1 (2022): 3–106. http://dx.doi.org/10.5840/studneoar20221911.
Full textAbstract:
I discuss the views on logic held by three early Nordic neo-Aristotelians — the Swedes Johannes Canuti Lenaeus (1573–1669) and Johannes Rudbeckius (1581–1646), and the Dane Caspar Bartholin (1585–1629). They all studied in Wittenberg (enrolled respectively in 1597, 1601, and 1604) and were exponents of protestant (Lutheran) scholasticism. The works I utilize are Janitores logici bini (1607) and Enchiridion logicum (1608) by Bartholin; Logica (1625) and Controversiae logices (1629) by Rudbeckius; and Logica peripatetica (1633) by Lenaeus. Rudbeckius’s and Lenaeus’s books were published much later than they were prepared. Rudbeckius wrote the first versions of his books in 1606, and the material for Lenaeus’s book had been prepared by 1607. Bartholin calls the treatment of the nature of logic the “first doorkeeper of logic”. To compare the views of the three neo-Aristotelians on this topic, I systematically investigate what they have to say about second notions, the subject of logic, the internal and external goal of logic, and the definition of logic. I also compare their approaches with those of Jacob Martini (teacher of Rudbeckius and Bartholin) and Iacopo Zabarella (an intellectual predecessor of all three).
6
Feferman, Solomon. "Logic, Logics, and Logicism." Notre Dame Journal of Formal Logic 40, no. 1 (January 1999): 31–54. http://dx.doi.org/10.1305/ndjfl/1039096304.
Full text
7
Mott, Peter. "Default non-monotonic logic." Knowledge Engineering Review 3, no. 4 (December 1988): 265–84. http://dx.doi.org/10.1017/s0269888900004586.
Full textAbstract:
AbstractThis paper is a review of certain non-monotonic logics, which I call default non-monotonic logics. These are logics which exploit failure to prove. How each logic uses this basic idea is explained, and examples given. The emphasis is on leading ideas explained through examples: technical detail is avoided. Four non-monotonic logics are discussed: Reiter's default logic, McCarthy's circumscription, McDermott's modal non-monotonic logic, and Clarks's completed database. The first two are treated in some detail. The recent Hanks-McDermott criticism of non-monotonic logic is discussed, and some conclusions drawn about the prospects for non-monotonic logic. Recommendations for further reading are given.
8
Francez, Nissim. "Bilateral Connexive Logic." Logics 1, no. 3 (August 4, 2023): 157–62. http://dx.doi.org/10.3390/logics1030008.
Full textAbstract:
This paper proposes a bilateral analysis of connexivity, presenting a bilateral natural deduction system for a weak connexive logic. The proposed logic deviates from other connexive logics and other bilateral logics in the following respects: (1) The logic induces a difference in meaning between inner and outer occurrences of negation in the connexive axioms. (2) The logic allows incoherence—assertion and denial of the same formula—while still being non-trivial.
9
Golan, Rea, and Ulf Hlobil. "Minimally Nonstandard K3 and FDE." Australasian Journal of Logic 19, no. 5 (December 20, 2022): 182–213. http://dx.doi.org/10.26686/ajl.v19i5.7540.
Full textAbstract:
Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to classical logic. We give semantic and sequent-calculus formulations of these logics, and we highlight some reasons why these logics may be interesting in their own right.
10
MA, MINGHUI, and HANS VAN DITMARSCH. "DYNAMIC GRADED EPISTEMIC LOGIC." Review of Symbolic Logic 12, no. 4 (July 12, 2019): 663–84. http://dx.doi.org/10.1017/s1755020319000285.
Full textAbstract:
AbstractGraded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.
11
Mruczek-Nasieniewska, Krystyna, and Marek Nasieniewski. "A Kotas-Style Characterisation of Minimal Discussive Logic." Axioms 8, no. 4 (October 1, 2019): 108. http://dx.doi.org/10.3390/axioms8040108.
Full textAbstract:
In this paper, we discuss a version of discussive logic determined by a certain variant of Jaśkowski’s original model of discussion. The obtained system can be treated as the minimal discussive logic. It is determined by frames with serial accessibility relation. As the smallest one, this logic can be treated as a basis which could be extended to richer discussive logics that are obtained by varying accessibility relation and resulting in a lattice of discussive logics. One has to remember that while formulating discussive logics there is no one-to-one determination of discussive logics by modal logics. For example, it is proved that Jaśkowski’s logic D 2 can be expressed by other than S 5 modal logics. In this paper we consider a deductive system for the sketchily described minimal logic. While formulating the deductive system, we apply a method of Kotas that was used to axiomatize D 2 . The obtained system determines a logic D 0 as a set of theses that is contained in D 2 . Moreover, any discussive logic that would be expressed by means of the provided model of discussion would contain D 0 , so it is the smallest discussive logic.
12
Kent, Pamela, and Dennis van Liempd. "Linking Corporate Institutional Logics and Moral Reasoning – Evidence from Large Danish Audit Firms." management revue 32, no. 1 (2021): 53–83. http://dx.doi.org/10.5771/0935-9915-2021-1-53.
Full textAbstract:
This paper examines whether organizational levels of owner/partner, CPA manager, supervisor and other audit staff are associated with institutional logics of auditors in large Danish audit firms. Our findings identify the presence of the professional logic and commercial logic with the professional logic being two explicit logics of a fiduciary and a technical-expertise logic. The organizational levels of CPA manager, supervisor and other staff are significant in explaining the presence of the technical-expertise logic, but not the fiduciary logic. Higher moral reasoning of auditors and being a female are significantly associated with the presence of the fiduciary logic. All four organizational levels are significant in explaining the identified commercial logic with further tests indicating that partners place more emphasis than supervisors on the commercial logic. Additional tests examine whether moral reasoning is associated with the professional fiduciary, professional technical-expertise and commercial logics and whether organizational levels explain moral reasoning. We find that a higher professional fiduciary logic is associated with higher auditor moral reasoning. In contrast, lower moral reasoning is associated with higher professional technical-expertise and commercial logics. In addition, increased audit experience is associated with lower moral reasoning.
13
Kent, Pamela, and Dennis van Liempd. "Linking Corporate Institutional Logics and Moral Reasoning – Evidence from Large Danish Audit Firms." management revue 32, no. 1 (2021): 54–84. http://dx.doi.org/10.5771/0935-9915-2021-1-54.
Full textAbstract:
This paper examines whether organizational levels of owner/partner, CPA manager, supervisor and other audit staff are associated with institutional logics of auditors in large Danish audit firms. Our findings identify the presence of the professional logic and commercial logic with the professional logic being two explicit logics of a fiduciary and a technical-expertise logic. The organizational levels of CPA manager, supervisor and other staff are significant in explaining the presence of the technical-expertise logic, but not the fiduciary logic. Higher moral reasoning of auditors and being a female are significantly associated with the presence of the fiduciary logic. All four organizational levels are significant in explaining the identified commercial logic with further tests indicating that partners place more emphasis than supervisors on the commercial logic. Additional tests examine whether moral reasoning is associated with the professional fiduciary, professional technical-expertise and commercial logics and whether organizational levels explain moral reasoning. We find that a higher professional fiduciary logic is associated with higher auditor moral reasoning. In contrast, lower moral reasoning is associated with higher professional technical-expertise and commercial logics. In addition, increased audit experience is associated with lower moral reasoning.
14
Cloutier, Charlotte, and Ann Langley. "The Logic of Institutional Logics." Journal of Management Inquiry 22, no. 4 (January 24, 2013): 360–80. http://dx.doi.org/10.1177/1056492612469057.
Full text
15
Boolos, George. "Logic, Logic, and Logic." History and Philosophy of Logic 21, no. 3 (September 2000): 223–29. http://dx.doi.org/10.1080/01445340051095856.
Full text
16
BLUTE, R., J. R. B. COCKETT, and R. A. G. SEELY. "The logic of linear functors." Mathematical Structures in Computer Science 12, no. 4 (August 2002): 513–39. http://dx.doi.org/10.1017/s0960129502003717.
Full textAbstract:
This paper describes a family of logics whose categorical semantics is based on functors with structure rather than on categories with structure. This allows the consideration of logics that contain possibly distinct logical subsystems whose interactions are mediated by functorial mappings. For example, within one unified framework, we shall be able to handle logics as diverse as modal logic, ordinary linear logic, and the ‘noncommutative logic’ of Abrusci and Ruet, a variant of linear logic that has both commutative and noncommutative connectives.Although this paper will not consider in depth the categorical basis of this approach to logic, preferring instead to emphasise the syntactic novelties that it generates in the logic, we shall focus on the particular case when the logics are based on a linear functor, in order to give a definite presentation of these ideas. However, it will be clear that this approach to logic has considerable generality.
17
Kuznetsov, Stepan. "Action Logic is Undecidable." ACM Transactions on Computational Logic 22, no. 2 (May 15, 2021): 1–26. http://dx.doi.org/10.1145/3445810.
Full textAbstract:
Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. One of the operations of this logic is the Kleene star, which is axiomatized by an induction scheme. For a stronger system that uses an -rule instead (infinitary action logic), Buszkowski and Palka (2007) proved -completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by Kozen in 1994. In this article, we show that it is undecidable, more precisely, -complete. We also prove the same undecidability results for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.
18
Firdaus, Qusthan A. H. "What is This Thing Called Adat Logic?" Jurnal Filsafat 32, no. 1 (June 9, 2022): 58. http://dx.doi.org/10.22146/jf.70202.
Full textAbstract:
The notion of adat (or custom) law does not encourage people in philosophy to reveal its logic. This article aims to investigate the possibility of adat logic, its variety, and a possible common ground or thesis among its own kinds. In general, the adat logic means the true contradiction between the rigidity and the reflexibility of custom. In other words, it resembles the idea of dialetheia in modern logic, but it does not mean that the adat logic is a subdivision of the former. To seek a thesis of adat logic is to discuss the Javanese and Minangkabaunese adat logics, and I transform both logics into some notations for the sake of avoiding unnecessary linguistic challenges and hurdles. Thus, I insert each notation of a particular adat logic into the general notation of adat logic. By doing so, I wish to discover a common ground between some different adat logics.
19
PUNČOCHÁŘ, VÍT. "SUBSTRUCTURAL INQUISITIVE LOGICS." Review of Symbolic Logic 12, no. 2 (February 1, 2019): 296–330. http://dx.doi.org/10.1017/s1755020319000017.
Full textAbstract:
AbstractThis paper shows that any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic. We introduce a relational semantic framework for substructural logics that enables us to define the notion of an inquisitive extension of λ, denoted as ${\lambda ^?}$, for any logic λ that is at least as strong as BSL. A general theory of these “inquisitive extensions” is worked out. In particular, it is shown how to axiomatize ${\lambda ^?}$, given the axiomatization of λ. Furthermore, the general theory is applied to some prominent logical systems in the class: classical logic Cl, intuitionistic logic Int, and t-norm based fuzzy logics, including for example Łukasiewicz fuzzy logic Ł. For the inquisitive extensions of these logics, axiomatization is provided and a suitable semantics found.
20
Sen, Jayanta, and M. K. Chakraborty. "Linear Logic and Lukasiewicz ℵ0- Valued Logic: A Logico-Algebraic Study." Journal of Applied Non-Classical Logics 11, no. 3-4 (January 2001): 313–29. http://dx.doi.org/10.3166/jancl.11.313-329.
Full text
21
Gadducci, Fabio, and Ugo Montanari. "Comparing logics for rewriting: rewriting logic, action calculi and tile logic." Theoretical Computer Science 285, no. 2 (August 2002): 319–58. http://dx.doi.org/10.1016/s0304-3975(01)00362-0.
Full text
22
HUET, GÉRARD. "Special issue on ‘Logical frameworks and metalanguages’." Journal of Functional Programming 13, no. 2 (March 2003): 257–60. http://dx.doi.org/10.1017/s0956796802004549.
Full textAbstract:
There is both a great unity and a great diversity in presentations of logic. The diversity is staggering indeed – propositional logic, first-order logic, higher-order logic belong to one classification; linear logic, intuitionistic logic, classical logic, modal and temporal logics belong to another one. Logical deduction may be presented as a Hilbert style of combinators, as a natural deduction system, as sequent calculus, as proof nets of one variety or other, etc. Logic, originally a field of philosophy, turned into algebra with Boole, and more generally into meta-mathematics with Frege and Heyting. Professional logicians such as Gödel and later Tarski studied mathematical models, consistency and completeness, computability and complexity issues, set theory and foundations, etc. Logic became a very technical area of mathematical research in the last half century, with fine-grained analysis of expressiveness of subtheories of arithmetic or set theory, detailed analysis of well-foundedness through ordinal notations, logical complexity, etc. Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal specifications and proofs of correctness of computer programs. This gave rise to more exotic logics, such as dynamic logic, Hoare-style logic of axiomatic semantics, logics of partial values (such as Scott's denotational semantics and Plotkin's domain theory) or of partial terms (such as Feferman's free logic), etc. The first actual attempts at mechanisation of logical reasoning through the resolution principle (automated theorem proving) had been disappointing, but their shortcomings gave rise to a considerable body of research, developing detailed knowledge about equational reasoning through canonical simplification (rewriting theory) and proofs by induction (following Boyer and Moore successful integration of primitive recursive arithmetic within the LISP programming language). The special case of Horn clauses gave rise to a new paradigm of non-deterministic programming, called Logic Programming, developing later into Constraint Programming, blurring further the scope of logic. In order to study knowledge acquisition, researchers in artificial intelligence and computational linguistics studied exotic versions of modal logics such as Montague intentional logic, epistemic logic, dynamic logic or hybrid logic. Some others tried to capture common sense, and modeled the revision of beliefs with so-called non-monotonic logics. For the careful crafstmen of mathematical logic, this was the final outrage, and Girard gave his anathema to such “montres à moutardes”.
23
Majkic, Zoran. "Paraconsistent da Costa Weakening of Intuitionistic Negation: What does it mean?" International Journal of Pure Mathematics 9 (March 16, 2022): 35–48. http://dx.doi.org/10.46300/91019.2022.9.9.
Full textAbstract:
In this paper we consider the systems of weakening of intuitionistic negation logic mZ, introduced in [1], [2], which are developed in the spirit of da Costa's approach. We take a particular attention on the philosophical considerations of the paraconsistent mZ logic w.r.t. the constructive semantics of the intuitionistic logic, and we show that mZ is a subintuitionistic logic. Hence, we present the relationship between intuitionistic and paraconsistent subintuitionistic negation used in mZ. Then we present a significant number of examples for this subintuitionistic and paraconsistent mZ logics: Logic Programming with Fiting's fixpoint semantics for paraconsistent weakening of 3-valued Kleene's and 4-valued Belnap's logics. Moreover, we provide a canonical construction of infinitary-valued mZ logics and, in particular, the paraconsistent weakening of standard Zadeh's fuzzy logic and of the Godel-Dummet t-norm intermediate logics.
24
Koellner, Peter. "Strong Logics of First and Second Order." Bulletin of Symbolic Logic 16, no. 1 (March 2010): 1–36. http://dx.doi.org/10.2178/bsl/1264433796.
Full textAbstract:
AbstractIn this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing.
25
Schurz, Gerhard. "Why classical logic is privileged: justification of logics based on translatability." Synthese 199, no. 5-6 (November 1, 2021): 13067–94. http://dx.doi.org/10.1007/s11229-021-03367-2.
Full textAbstract:
AbstractIn Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages.
26
Devyatkin, Leonid Yu. "On the three-valued expansions of Kleene's logic." Logical Investigations 29, no. 2 (2023): 59–88. http://dx.doi.org/10.21146/2074-1472-2023-29-2-59-88.
Full textAbstract:
The paper is devoted to one of the most famous three-valued systems – Kleene's logic. The expressive capabilities of Kleene's logic and its three-valued expansions are described. We present two results. First, all possible three-valued expansions of Kleene's logic are found up to equivalence with respect to the mutual definability of connectives. It is shown that there are only twelve such expansions. This list includes both logics already known in the literature and completely new ones. For the found expansions, we describe the structure of the lattice ordered relative to the expressive power of its elements. Secondly, for Kleene's logic and its three-valued expansions we find how many extensions each of these logics has in the same language. Kleene's logic has only two proper extensions: the classical and the trivial ones. Generally, a three-valued logic in which Kleene's matrix is definable contains no more than three proper extensions: the classical one, the trivial one, and an intermediate logic, determined by the product of the the original logic's matrix and the matrix of classical logic in the same signature. Intermediate logics exist only for two types of three-valued expansions of Kleene's logic: in expansions equivalent to Łukasiewicz's logic, and in logics whose matrices contain both a bivalent submatrix, the universe of which consists of the classical truth values, and a submatrix, the universe of which consists the intermediate value alone. All three-valued expansions of Kleene's logic that do not preserve the classical values have only one extension of their own – the trivial one.
27
Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (June 1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.
Full textAbstract:
The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.
28
Dardinier, Thibault, and Peter Müller. "Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties." Proceedings of the ACM on Programming Languages 8, PLDI (June 20, 2024): 1485–509. http://dx.doi.org/10.1145/3656437.
Full textAbstract:
Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been generalized to prove also properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic), by proving the existence of (bad combinations of) executions. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre- and post-state for functional properties or pairs of pre- and post-states for non-interference. In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. The resulting logic is simple yet expressive: its judgments can express arbitrary program hyperproperties, a particular class of hyperproperties over the set of terminating executions of a program (including properties of individual program executions). By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic, including (hyper-)properties that no existing Hoare logic can express. We prove that Hyper Hoare Logic is sound and complete, and demonstrate that it captures important proof principles naturally. All our technical results have been proved in Isabelle/HOL.
29
Dahlmann, Frederik, and Johanne Grosvold. "Environmental Managers and Institutional Work: Reconciling Tensions of Competing Institutional Logics." Business Ethics Quarterly 27, no. 2 (February 27, 2017): 263–91. http://dx.doi.org/10.1017/beq.2016.65.
Full textAbstract:
ABSTRACT:Firms face a variety of institutional logics and one important question is how individuals within firms manage these logics. Environmental managers in particular face tensions in reconciling their firms’ commercial fortunes with demands for greater environmental responsiveness. We explore how institutional work enables environmental managers to respond to competing institutional logics. Drawing on repeated interviews with 55 firms, we find that environmental managers face competition between a market-based logic and an emerging environmental logic. We show that some environmental managers embed the environmental logic alongside the market logic through variations of creation and disruption, thus over time creating institutional change, which can result in blended logics. Others, however, pursue a strategy of status quo or disengagement through maintenance or other forms of disruption, where the two logics coexist in principle but not in practice; instead the market logic retains its dominance. We discuss the implications of our findings for research.
30
Widlok, Thomas, and Keith Stenning. "Seeking Common Cause between Cognitive Science and Ethnography: Alternative Logic in Cooperative Action." Journal of Cognition and Culture 18, no. 1-2 (March 28, 2018): 1–30. http://dx.doi.org/10.1163/15685373-12340027.
Full textAbstract:
Abstract Alternative logics have been invoked periodically to explain the systematically different modes of thought of the subjects of ethnography: one logic for ‘us’ and another for ‘them’. Recently anthropologists have cast doubt on the tenability of such an explanation of difference. In cognitive science, [Stenning and van Lambalgen, 2008] proposed that with the modern development of multiple logics, at least several logics are required for making sense of the cognitive processes of reasoning for different purposes and in different contexts. Alongside Classical logic (CL) — the logic of dispute), there is a need for a nonmonotonic logic (LP) which is a logic of cooperative communication. Here we propose that all people with various cultural backgrounds make use of multiple logics, and that difference should be captured as variation in the social contexts that call forth the different logics’ application. This contribution illustrates these ideas with reference to the ethnography of divination.
31
Маркин, В. И. "What trends in non-classical logic were anticipated by Nikolai Vasiliev?" Logical Investigations 19 (April 9, 2013): 122–35. http://dx.doi.org/10.21146/2074-1472-2013-19-0-122-135.
Full textAbstract:
In this paper we discuss a question about the trends in non-classical logic that were exactly anticipated by Niko- lai Vasiliev. We show the influence of Vasiliev’s Imaginary logic on paraconsistent logic. Metatheoretical relations between Vasiliev’s logical systems and many-valued predicate logics are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic and expressed certain ideas of modal and temporal logics.
32
Xiong, Liping, and Sumei Guo. "Representation and Reasoning about Strategic Abilities with ω-Regular Properties." Mathematics 9, no. 23 (November 27, 2021): 3052. http://dx.doi.org/10.3390/math9233052.
Full textAbstract:
Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*.
33
DYCK, Corey W. "THE PRIORITY OF JUDGING: KANT ON WOLFF’S GENERAL LOGIC." Estudos Kantianos [EK] 4, no. 02 (January 25, 2017): 99–118. http://dx.doi.org/10.36311/2318-0501.2016.v4n2.07.p99.
Full textAbstract:
One would be forgiven for suspecting that Kant did not think much of Christian Wolff’s contributions to logic. Wolff’s works on logic are, of course, implicated in Kant’s far-ranging verdict that the discipline has not taken a single step forward since Aristotle’s time, and Wolff in particular frequently comes up for criticism in Kant’s own lectures on the topic. In the Wiener Logik, for example, Kant is reported as referring to Wolff’s claim that the content of a concept can be completely analysed as “too dictatorial” and that as a result Wolff’s attempts to ground his philosophy on the precise definitions of concepts is “entirely false” (V-Lo/Wiener, AA 24: 917). Given this, it is to say the least surprising that (from the late 1770’s onwards1) Kant should regularly single out Wolff’s general logic in those lectures as “the best one has” (V-Lo/ Pölitz, AA 24: 509), “the best that one encounters” (V-Lo/Wiener, AA 24:796), or even simply “the best” (V-Lo/Busolt, AA 24: 613; cf. also Log 9: 20).2 Nor would this seem to be a sort of backhanded compliment, praising Wolff’s as only the best of a bad lot of modern general logics, since this high estimation is echoed by some of Kant’s closest disciples: so, we find unadulterated praise in L. H. Jakob’s preface to his Grundriß der allgemeinen Logik, where it is claimed “Wolff grasped the idea of a general logic exceedingly well,”3 a passage that is also approvingly quoted in Jäsche’s introduction to his edition of Kant’s Logik.
34
Avron, Arnon. "Natural 3-valued logics—characterization and proof theory." Journal of Symbolic Logic 56, no. 1 (March 1991): 276–94. http://dx.doi.org/10.2307/2274919.
Full textAbstract:
Many-valued logics in general and 3-valued logic in particular is an old subject which had its beginning in the work of Łukasiewicz [Łuk]. Recently there is a revived interest in this topic, both for its own sake (see, for example, [Ho]), and also because of its potential applications in several areas of computer science, such as proving correctness of programs [Jo], knowledge bases [CP] and artificial intelligence [Tu]. There are, however, a huge number of 3-valued systems which logicians have studied throughout the years. The motivation behind them and their properties are not always clear, and their proof theory is frequently not well developed. This state of affairs makes both the use of 3-valued logics and doing fruitful research on them rather difficult.Our first goal in this work is, accordingly, to identify and characterize a class of 3-valued logics which might be called natural. For this we use the general framework for characterizing and investigating logics which we have developed in [Av1]. Not many 3-valued logics appear as natural within this framework, but it turns out that those that do include some of the best known ones. These include the 3-valued logics of Łukasiewicz, Kleene and Sobociński, the logic LPF used in the VDM project, the logic RM3 from the relevance family and the paraconsistent 3-valued logic of [dCA]. Our presentation provides justifications for the introduction of certain connectives in these logics which are often regarded as ad hoc. It also shows that they are all closely related to each other. It is shown, for example, that Łukasiewicz 3-valued logic and RM3 (the strongest logic in the family of relevance logics) are in a strong sense dual to each other, and that both are derivable by the same general construction from, respectively, Kleene 3-valued logic and the 3-valued paraconsistent logic.
35
Kondratyev, Dmitry A. "Logic for reasoning about bugs in loops over data sequences (IFIL)." Modeling and Analysis of Information Systems 30, no. 3 (September 17, 2023): 214–33. http://dx.doi.org/10.18255/1818-1015-2023-3-214-233.
Full textAbstract:
Classic deductive verification is not focused on reasoning about program incorrectness. Reasoning about program incorrectness using formal methods is an important problem nowadays. Special logics such as Incorrectness Logic, Adversarial Logic, Local Completeness Logic, Exact Separation Logic and Outcome Logic have recently been proposed to address it. However, these logics have two disadvantages. One is that they are based on under-approximation approaches, while classic deductive verification is based on the over-approximation approach. One the other hand, the use of the classic approach requires defining loop invariants in a general case. The second disadvantage is that the use of generalized inference rules from these logics results in having to prove too complex formulas in simple cases. Our contribution is a new logic for solving these problems in the case of loops over data sequences. These loops are referred to as finite iterations. We call the proposed logic the Incorrectness Finite Iteration Logic (IFIL). We avoid defining invariants of finite iterations using a symbolic replacement of these loops with recursive functions. Our logic is based on special inference rules for finite iterations. These rules allow generating formulas with recursive functions corresponding to finite iterations. The validity of these formulas may indicate the presence of bugs in the finite iterations. This logic has been implemented in a new version of the C-lightVer system for deductive verification of C programs.
36
KAMIDE, NORIHIRO. "Embedding theorems for LTL and its variants." Mathematical Structures in Computer Science 25, no. 1 (December 2, 2014): 83–134. http://dx.doi.org/10.1017/s0960129514000048.
Full textAbstract:
In this paper, we prove some embedding theorems for LTL (linear-time temporal logic) and its variants:viz. some generalisations, extensions and fragments of LTL. Using these embedding theorems, we give uniform proofs of the completeness, cut-elimination and/or decidability theorems for LTL and its variants. The proposed embedding theorems clarify the relationships between some LTL-variations (for example, LTL, a dynamic topological logic, a fixpoint logic, a spatial logic, Prior's logic, Davies' logic and an NP-complete LTL) and some traditional logics (for example, classical logic, intuitionistic logic and infinitary logic).
37
Walker, Matt, Parssa Khazra, Anto Nanah Ji, Hongru Wang, and Franck van Breugel. "jpf-logic." ACM SIGSOFT Software Engineering Notes 48, no. 1 (January 10, 2023): 32–36. http://dx.doi.org/10.1145/3573074.3573083.
Full textAbstract:
We present jpf-logic, an extension of the model checker Java PathFinder (JPF). Our extension jpf-logic provides a framework to check properties expressed in temporal logics such as linear temporal logic (LTL) and computation tree logic (CTL). To support a logic in our framework, we (1) implement a parser for the logic, (2) develop a hierarchy of classes that represent the abstract syntax of the logic and implement a transformation from parse trees of formulas to the corresponding abstract syntax trees, and (3) implement a model checking algorithm that takes as input an abstract syntax tree of a formula and a partial transition system. The latter represents a model of the Java application. All three components have been implemented for CTL. The first two have been implemented for LTL.
38
Estrada-González, Luis. "Logic taking care of itself: the case of connexive logic." Principia: an international journal of epistemology 28, no. 1 (July 10, 2024): 155–65. http://dx.doi.org/10.5007/1808-1711.2024.e96733.
Full textAbstract:
Logic is an excellent tool for reasoning about most philosophical topics, including logical issues themselves. Discussions about the validity or otherwise of certain principles have been widespread throughout the history of logic. This chapter exemplifies that with the analysis of the debate surrounding connexive logics. In connexive logics, certain principles involving mainly negation and implication hold good, whereas they are not valid in most well-known logics. Despite their intuitiveness, the connexive principles quickly lead to contradictions and even to triviality, i.e. to the truth of every proposition. This chapter surveys the main arguments against the connexive principles and discusses some prospects for challenging those arguments and endorsing the connexive principles.
39
Hannula, Miika, Juha Kontinen, and Jonni Virtema. "Polyteam semantics." Journal of Logic and Computation 30, no. 8 (September 23, 2020): 1541–66. http://dx.doi.org/10.1093/logcom/exaa048.
Full textAbstract:
Abstract Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.
40
Hu, Zhi Ming, Zhong Qi Wang, Ning Li, and Hui Ping Wang. "Description Logics in Information Semantic Integration for Product Design and Manufacturing." Advanced Materials Research 542-543 (June 2012): 251–54. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.251.
Full textAbstract:
In the process of information semantic integration for product design and manufacturing, it is very important to express the product information semantic. Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and a decidable subset of first-order logic. Firstly, by analyzing the characteristics of product information, proposed a semantic information description framework based on description logics for product information integration, which is divided into three levels: basic description logic, classic extended logic and unusual extended logic. Then, in the framework, reducer was taken for example to illustrate the application of their description logic in product design and manufacturing formal semantic information. Finally, based on description logic, discussed reasoning problems of product design and manufacturing information.
41
Demey, Lorenz. "Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics." Axioms 10, no. 3 (June 22, 2021): 128. http://dx.doi.org/10.3390/axioms10030128.
Full textAbstract:
Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distinguish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic.
42
BESSON, CORINE. "EXTERNALISM, INTERNALISM, AND LOGICAL TRUTH." Review of Symbolic Logic 2, no. 1 (March 2009): 1–29. http://dx.doi.org/10.1017/s1755020309090091.
Full textAbstract:
The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist--internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order logic is a free logic—a second order logic free of existential commitments for natural kind nouns, while an externalist second-order logic is not free of existential commitments for natural kind nouns—it is existentially committed.
43
Rimatskiy, V. V. "Admissible Inference Rules and Semantic Property of Modal Logics." Bulletin of Irkutsk State University. Series Mathematics 37 (2021): 104–17. http://dx.doi.org/10.26516/1997-7670.2021.37.104.
Full textAbstract:
Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.
44
ALIZADEH, MAJID, FARZANEH DERAKHSHAN, and HIROAKIRA ONO. "UNIFORM INTERPOLATION IN SUBSTRUCTURAL LOGICS." Review of Symbolic Logic 7, no. 3 (May 27, 2014): 455–83. http://dx.doi.org/10.1017/s175502031400015x.
Full textAbstract:
AbstractUniform interpolation property of a given logic is a stronger form of Craig’s interpolation property where both pre-interpolant and post-interpolant always exist uniformly for any provable implication in the logic. It is known that there exist logics, e.g., modal propositional logic S4, which have Craig’s interpolation property but do not have uniform interpolation property. The situation is even worse for predicate logics, as classical predicate logic does not have uniform interpolation property as pointed out by L. Henkin.In this paper, uniform interpolation property of basic substructural logics is studied by applying the proof-theoretic method introduced by A. Pitts (Pitts, 1992). It is shown that uniform interpolation property holds even for their predicate extensions, as long as they can be formalized by sequent calculi without contraction rules. For instance, uniform interpolation property of full Lambek predicate calculus, i.e., the substructural logic without any structural rule, and of both linear and affine predicate logics without exponentials are proved.
45
Barrio, Eduardo, Lucas Rosenblatt, and Diego Tajer. "The Logics of Strict-Tolerant Logic." Journal of Philosophical Logic 44, no. 5 (December 31, 2014): 551–71. http://dx.doi.org/10.1007/s10992-014-9342-6.
Full text
46
Kooi, Barteld, and Allard Tamminga. "Three-valued Logics in Modal Logic." Studia Logica 101, no. 5 (August 21, 2012): 1061–72. http://dx.doi.org/10.1007/s11225-012-9420-0.
Full text
47
Jin, Chen. "A review on multiple-valued logic circuits." Applied and Computational Engineering 43, no. 1 (February 26, 2024): 322–26. http://dx.doi.org/10.54254/2755-2721/43/20230857.
Full textAbstract:
Since the traditional binary logic has several disadvantages including inaccuracy, high complexity, and limited applications. Multiple-Valued Logic (MVL), which can store more information in one digit than binary logics, require less number of logic gates and take the third value in practical logic problems, is developed and introduced. More information stored per digit leads to higher computational efficiency. Less logic gates results in more spaces on the circuit board. Considering the third value means higher accuracy. In this research, some examples of different MVL circuit are designed to give a rough picture of current research in this domain. These designs are based on ternary and quaternary logics rather than binary logics. Besides, reliability evaluation through mathematical approach is presented in order to prove that the new design is more preferable. This can be carried out with mathematical analysis such as calculating a matrix that reflects its reliability, and simulating different designs to obtain certain values and comparing them with each other. Despite facing various challenges, including complicated physical implementation and difficulty to modulate the signals. This means that there is still potential of further research in this domain of logic circuits. This result in the conclusion that the MVL logic circuits will replace the conventional binary logic circuits in the future, and probably that decimal logic would be developed and no binary-to-decimal conversion unit will be required.
48
Metcalfe, George, and Franco Montagna. "Substructural fuzzy logics." Journal of Symbolic Logic 72, no. 3 (September 2007): 834–64. http://dx.doi.org/10.2178/jsl/1191333844.
Full textAbstract:
AbstractSubstructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0, 1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) V ((B → A)∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MIX and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1].
49
Fujio, Mitsuhiko. "A Comparison of Implications in Orthomodular Quantum Logic—Morphological Analysis of Quantum Logic." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/259541.
Full textAbstract:
Morphological operators are generalized to lattices as adjunction pairs (Serra, 1984; Ronse, 1990; Heijmans and Ronse, 1990; Heijmans, 1994). In particular, morphology for set lattices is applied to analyze logics through Kripke semantics (Bloch, 2002; Fujio and Bloch, 2004; Fujio, 2006). For example, a pair of morphological operators as an adjunction gives rise to a temporalization of normal modal logic (Fujio and Bloch, 2004; Fujio, 2006). Also, constructions of models for intuitionistic logic or linear logics can be described in terms of morphological interior and/or closure operators (Fujio and Bloch, 2004). This shows that morphological analysis can be applied to various non-classical logics. On the other hand, quantum logics are algebraically formalized as orhomodular or modular ortho-complemented lattices (Birkhoff and von Neumann, 1936; Maeda, 1980; Chiara and Giuntini, 2002), and shown to allow Kripke semantics (Chiara and Giuntini, 2002). This suggests the possibility of morphological analysis for quantum logics. In this article, to show an efficiency of morphological analysis for quantum logic, we consider the implication problem in quantum logics (Chiara and Giuntini, 2002). We will give a comparison of the 5 polynomial implication connectives available in quantum logics.
50
Standefer, Shawn. "Tracking reasons with extensions of relevant logics." Logic Journal of the IGPL 27, no. 4 (June 25, 2019): 543–69. http://dx.doi.org/10.1093/jigpal/jzz018.
Full textAbstract:
Abstract In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics.