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Journal articles on the topic 'The rules of logic'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Rimatskiy, V. V. "Globally Admissible Inference Rules." Bulletin of Irkutsk State University. Series Mathematics 42 (2022): 138–60. http://dx.doi.org/10.26516/1997-7670.2022.42.138.

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Setting the basic rules of inference is fundamental to logic. The most general variant of possible inference rules are admissible inference rules: in logic 𝐿, a rule of inference is admissible if the set of theorems 𝐿 is closed with respect to this rule. The study of admissible inference rules was stimulated by Friedman’s problem: Is there an algorithm for recognizing the admissibility of an inference rule in intuitionistic logic? For a wide class of non-classical logics the problem of recognizing with respect to the admissibility of inference rules was solved in 1980s. Another way of describi

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2

Rimatskiy, V. V. "https://mathizv.isu.ru/en/article?id=1516." Bulletin of Irkutsk State University. Series Mathematics 50 (2024): 152–69. https://doi.org/10.26516/1997-7670.2024.50.152.

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Setting the basic rules of inference is fundamental to logic. The most general variant of possible inference rules are admissible inference rules:in logic L, a rule of inference is admissible if the set of theorems L is closed with respect to this rule. The study of admissible inference rules was stimulated by the formulation of problems about decidability by admissibility (Friedman) and the presence of a finite basis of admissible rules (Kuznetsov) in Int logic. In the early 2000s, for most basic non-classical logics and some tabular logics, the Fridman-Kuznetsov problem was solved by describ

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3

Evans, R., M. Sergot, and A. Stephenson. "Formalizing Kant’s Rules." Journal of Philosophical Logic 49, no. 4 (2019): 613–80. http://dx.doi.org/10.1007/s10992-019-09531-x.

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AbstractThis paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These acts are not propositions; they do not have truth-values. Our formalization is related to the

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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.

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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 improvem

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Batens, Diderik. "Devising the set of abnormalities for a given defeasible rule." Logical Investigations 26, no. 1 (2020): 9–35. http://dx.doi.org/10.21146/2074-1472-2020-26-1-9-35.

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Devising adaptive logics usually starts with a set of abnormalities and a deductive logic. Where the adaptive logic is ampliative, the deductive logic is the lower limit logic, the rules of which are unconditionally valid. Where the adaptive logic is corrective, the deductive logic is the upper limit logic, the rules of which are valid in case the premises do not require any abnormalities to be true. In some cases, the idea for devising an adaptive logic does not relate to a set of abnormalities, but to one or more defeasible rules, and perhaps also to one of the deductive logics. Defeasible r

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Thirumaran., M., E. Ilavarasan., K. Thanigaivel., and S. Abarna. "BUSINESS RULE MANAGEMENT FRAMEWORK FOR ENTERPRISE WEB SERVICES." International Journal on Web Service Computing (IJWSC) 1, no. 2 (2010): 15–29. https://doi.org/10.5281/zenodo.3936393.

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Making a business rule extraction more dynamic is an open issue, and we think it is feasible if we decompose the business process structure in a set of rules, each of them representing a transition of the business process. As a consequence the business process engine can be realized by reusing and integrating an existing Rule Engine. We are proposing a way for extracting the business rules and then to modify it at the runtime. Business rules specifies the constraints that affect the behaviors and also specifies the derivation of conditions that affect the execution flow. The rules can be extra

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Thirumaran., M., E. Ilavarasan., K. Thanigaivel., and S. Abarna. "BUSINESS RULE MANAGEMENT FRAMEWORK FOR ENTERPRISE WEB SERVICES." International Journal on Web Service Computing (IJWSC) 1, no. 2 (2010): 15–29. https://doi.org/10.5281/zenodo.3345678.

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Making a business rule extraction more dynamic is an open issue, and we think it is feasible if we decompose the business process structure in a set of rules, each of them representing a transition of the business process. As a consequence the business process engine can be realized by reusing and integrating an existing Rule Engine. We are proposing a way for extracting the business rules and then to modify it at the runtime. Business rules specifies the constraints that affect the behaviors and also specifies the derivation of conditions that affect the execution flow. The rules can be extra

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Jeřábek, Emil. "Canonical rules." Journal of Symbolic Logic 74, no. 4 (2009): 1171–205. http://dx.doi.org/10.2178/jsl/1254748686.

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AbstractWe develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia theorem and the theory of modal companions to systems of

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9

MAHER, MICHAEL J. "Propositional defeasible logic has linear complexity." Theory and Practice of Logic Programming 1, no. 6 (2001): 691–711. http://dx.doi.org/10.1017/s1471068401001168.

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Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.

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Kondratyev, Dmitry A. "Logic for reasoning about bugs in loops over data sequences (IFIL)." Modeling and Analysis of Information Systems 30, no. 3 (2023): 214–33. http://dx.doi.org/10.18255/1818-1015-2023-3-214-233.

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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 requ

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11

BEZHANISHVILI, GURAM, NICK BEZHANISHVILI, and ROSALIE IEMHOFF. "STABLE CANONICAL RULES." Journal of Symbolic Logic 81, no. 1 (2016): 284–315. http://dx.doi.org/10.1017/jsl.2015.54.

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AbstractWe introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules. We also define stable multi-conclusion consequence relations and stable logics and prove that these systems have the finite model property. We conclude the paper with a number of examples of stable and nonstable systems, and show how to axiomatize them.

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12

Rauch, Jan. "Logic of Association Rules." Applied Intelligence 22, no. 1 (2005): 9–28. http://dx.doi.org/10.1023/b:apin.0000047380.15356.7a.

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13

GIRARD, JEAN-YVES. "Locus Solum: From the rules of logic to the logic of rules." Mathematical Structures in Computer Science 11, no. 3 (2001): 301–506. http://dx.doi.org/10.1017/s096012950100336x.

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Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (…) An-Fang was near a city, the only living city with a pre-atomic name (…) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead Lady of Clown Town, 1964.

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DZIK, WOJCIECH, and PIOTR WOJTYLAK. "UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS." Review of Symbolic Logic 12, no. 1 (2018): 37–61. http://dx.doi.org/10.1017/s1755020318000011.

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AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) struc

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15

ANTOY, SERGIO, and MICHAEL HANUS. "Default rules for Curry." Theory and Practice of Logic Programming 17, no. 2 (2016): 121–47. http://dx.doi.org/10.1017/s1471068416000168.

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AbstractIn functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional

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Ramanujam, R., Vaishnavi Sundararajan, and S. P. Suresh. "The complexity of disjunction in intuitionistic logic." Journal of Logic and Computation 30, no. 1 (2020): 421–45. http://dx.doi.org/10.1093/logcom/exaa018.

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Abstract We study procedures for the derivability problem of fragments of intuitionistic logic. Intuitionistic logic is known to be PSPACE-complete, with implication being one of the main contributors to this complexity. In fact, with just implication alone, we still have a PSPACE-complete logic. We study fragments of intuitionistic logic with restricted implication and develop algorithms for these fragments which are based on the proof rules. We identify a core fragment whose derivability is solvable in linear time. Adding disjunction elimination to this core gives a logic which is solvable i

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Stärk, Robert, and Stanislas Nanchen. "A Logic for Abstract State Machines." JUCS - Journal of Universal Computer Science 7, no. (11) (2001): 980–1005. https://doi.org/10.3217/jucs-007-11-0980.

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We introduce a logic for non distributed, deterministic Abstract State Machines with parallel function updates. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on an atomic predicate for function updates and on a definedness predicate for the termination of the evaluation of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms t

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18

Sambin, Giovanni, Giulia Battilotti, and Claudia Faggian. "Basic logic: reflection, symmetry, visibility." Journal of Symbolic Logic 65, no. 3 (2000): 979–1013. http://dx.doi.org/10.2307/2586685.

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AbstractWe introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic. quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility.A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with a metalinguistic link between assertions, and if its syntactic inference rules are obtained

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19

KOWALSKI, ROBERT, and FARIBA SADRI. "Programming in logic without logic programming." Theory and Practice of Logic Programming 16, no. 3 (2016): 269–95. http://dx.doi.org/10.1017/s1471068416000041.

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AbstractIn previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions, and other events are represented with timestamps. But in the operational semantics (OS), for the sake

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20

Piazza, Mario. "Exchange rules." Journal of Symbolic Logic 66, no. 2 (2001): 509–16. http://dx.doi.org/10.2307/2695028.

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AbstractIn this paper, we show by a proof-theoretical argument that in a logic without structural rules, that is in noncommutative linear logic with exponentials, every formula A for which exchange rules (and weakening and contraction as well) are admissible is provably equivalent to? A. This property shows that the expressive power of “noncommutative exponentials” is much more important than that of “commutative exponentials”.

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21

MAHER, MICHAEL J., ANDREW ROCK, GRIGORIS ANTONIOU, DAVID BILLINGTON, and TRISTAN MILLER. "EFFICIENT DEFEASIBLE REASONING SYSTEMS." International Journal on Artificial Intelligence Tools 10, no. 04 (2001): 483–501. http://dx.doi.org/10.1142/s0218213001000623.

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For many years, the non-montonic reasoning community has focussed on highly expressive logics. Such logics have turned out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic: a query answering system employing a backward-chaining approach, and a forward-chaining implementation that computes all conclusions. Our experimental evaluation demonstrates that the systems can deal w

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22

Polkowski, Lech. "A Note on 3-valued Rough Logic Accepting Decision Rules." Fundamenta Informaticae 61, no. 1 (2004): 37–45. https://doi.org/10.3233/fun-2004-61104.

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Rough sets carry, intuitively, a 3-valued logical structure related to the three regions into which any rough set x divides the universe., viz., the lower definable set i(x), the upper definable set c(x), and the boundary region c(x)\setminus i(x) witnessing the vagueness of associated knowledge. In spite of this intuition, the currently known way of relating rough sets and 3-valued logics is only via 3-valued Łukasiewicz algebras (Pagliani) that endow spaces of disjoint representations of rough sets with its structure. Here, we point to a 3-valued rough logic RL of unary predicates in which v

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Brady, Ross T. "Normalized natural deduction systems for some relevant logics I: The logic DW." Journal of Symbolic Logic 71, no. 1 (2006): 35–66. http://dx.doi.org/10.2178/jsl/1140641162.

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Fitch-style natural deduction was first introduced into relevant logic by Anderson in [1960], for the sentential logic E of entailment and its quantincational extension EQ. This was extended by Anderson and Belnap to the sentential relevant logics R and T and some of their fragments in [ENT1], and further extended to a wide range of sentential and quantified relevant logics by Brady in [1984]. This was done by putting conditions on the elimination rules, →E, ~E, ⋁E and ∃E, pertaining to the set of dependent hypotheses for formulae used in the application of the rule. Each of these rules were s

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RASGA, JOÃO, CRISTINA SERNADAS, and AMÍLCAR SERNADAS. "PRESERVATION OF ADMISSIBLE RULES WHEN COMBINING LOGICS." Review of Symbolic Logic 9, no. 4 (2016): 641–63. http://dx.doi.org/10.1017/s1755020316000241.

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AbstractAdmissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics, under mild conditions. A weak form of structural completeness is proved to be preserved by the combination. Decidability of the set of admissible rules is also shown to be preserved, with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.

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Boricic, Marija. "Inference rules for probability logic." Publications de l'Institut Math?matique (Belgrade) 100, no. 114 (2016): 77–86. http://dx.doi.org/10.2298/pim1614077b.

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Gentzen?s and Prawitz?s approach to deductive systems, and Carnap?s and Popper?s treatment of probability in logic were two fruitful ideas of logic in the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized by means of inference rules, we introduce a system of inference rules based on the traditional proof-theoretic principles enabling to work with each form of probabilized propositional formulae. Namely, for each propositional connective, we define at least one introduction and one elimination rule, over the formula

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26

Humberstone, L., and D. Makinson. "Intuitionistic Logic and Elementary Rules." Mind 120, no. 480 (2011): 1035–51. http://dx.doi.org/10.1093/mind/fzr076.

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Viry, Patrick. "Equational rules for rewriting logic." Theoretical Computer Science 285, no. 2 (2002): 487–517. http://dx.doi.org/10.1016/s0304-3975(01)00366-8.

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28

Duch, Wlodzislaw. "Rules, similarity, and threshold logic." Behavioral and Brain Sciences 28, no. 1 (2005): 23. http://dx.doi.org/10.1017/s0140525x05320012.

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Jerabek, E. "Admissible Rules of Lukasiewicz Logic." Journal of Logic and Computation 20, no. 2 (2010): 425–47. http://dx.doi.org/10.1093/logcom/exp078.

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OLKHOVIKOV, GRIGORY K., and PETER SCHROEDER-HEISTER. "ON FLATTENING ELIMINATION RULES." Review of Symbolic Logic 7, no. 1 (2014): 60–72. http://dx.doi.org/10.1017/s1755020313000385.

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AbstractIn proof-theoretic semantics of intuitionistic logic it is well known that elimination rules can be generated from introduction rules in a uniform way. If introduction rules discharge assumptions, the corresponding elimination rule is a rule of higher level, which allows one to discharge rules occurring as assumptions. In some cases, these uniformly generated elimination rules can be equivalently replaced with elimination rules that only discharge formulas or do not discharge any assumption at all—they can be flattened in a terminology proposed by Read. We show by an example from propo

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31

Citkin, Alex. "Deductive systems with unified multiple-conclusion rules." Logical Investigations 26, no. 2 (2020): 87–105. http://dx.doi.org/10.21146/2074-1472-2020-26-2-87-105.

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Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and are being treated in the same way. The suggested approach is based on the ideas of Ƚukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. A special attention is paid to the logics in which each proposition is either accepted or rejected.

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Visser, Albert. "Rules and Arithmetics." Notre Dame Journal of Formal Logic 40, no. 1 (1999): 116–40. http://dx.doi.org/10.1305/ndjfl/1039096308.

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Pudlák, Pavel. "Quantum deduction rules." Annals of Pure and Applied Logic 157, no. 1 (2009): 16–29. http://dx.doi.org/10.1016/j.apal.2008.09.017.

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Rimatskii, Vitalii V. "Explicit basis for admissible rules in K-saturated tabular logics." Discrete Mathematics and Applications 33, no. 2 (2023): 105–15. http://dx.doi.org/10.1515/dma-2023-0011.

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Vistrup, Max, Michael Sammler, and Ralf Jung. "Program Logics à la Carte." Proceedings of the ACM on Programming Languages 9, POPL (2025): 300–331. https://doi.org/10.1145/3704847.

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Program logics have proven a successful strategy for verification of complex programs. By providing local reasoning and means of abstraction and composition, they allow reasoning principles for individual components of a program to be combined to prove guarantees about a whole program. Crucially, these components and their proofs can be reused. However, this reuse is only available once the program logic has been defined. It is a frustrating fact of the status quo that whoever defines a new program logic must establish every part, both semantics and proof rules, from scratch. In spite of progr

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Rahman, Fadhlur, and Mohammad Kholid. "In the Realm of Reason: Al-Fârâbî's Logic and Language Paradigm." International Journal of Islamic Thought and Humanities 4, no. 1 (2025): 74–80. https://doi.org/10.54298/ijith.v4i1.389.

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Al-Farabi, an Islamic philosopher, focused on the correlation between logic and language, particularly regarding the process of reasoning. He classified logic into eight components, which align with the eight books of the Aristotelian Organon, and delineated logic as a system of rules governing thought. He asserted that the objectives of logic are to govern and direct reason towards correct thinking, establish measures to prevent mistakes and assign significance to comprehensible acknowledgments of error. As Aristotle's logic encompasses a set of methods aimed at effectively persuading others,

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Brady, Ross T. "Simple Gentzenizations for the normal formulae of contraction-less logics." Journal of Symbolic Logic 61, no. 4 (1996): 1321–46. http://dx.doi.org/10.2307/2275819.

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In [1], we established Gentzenizations for a good range of relevant logics with distribution, but, in the process, we added inversion rules, which involved extra structural connectives, and also added the sentential constant t. Instead of eliminating them, we used conservative extension results to relate them back to the original logics. In [4], we eliminated the inversion rules and t and established a much simpler Gentzenization for the weak sentential relevant logic DW, and also for its quantificational extension DWQ, but a restriction to normal formulae (defined below) was required to enabl

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CHIA, HENRY WAI-KIT, and CHEW-LIM TAN. "NEURAL LOGIC NETWORK LEARNING USING GENETIC PROGRAMMING." International Journal of Computational Intelligence and Applications 01, no. 04 (2001): 357–68. http://dx.doi.org/10.1142/s1469026801000299.

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Neural Logic Networks or Neulonets are hybrids of neural networks and expert systems capable of representing complex human logic in decision making. Each neulonet is composed of rudimentary net rules which themselves depict a wide variety of fundamental human logic rules. An early methodology employed in neulonet learning for pattern classification involved weight adjustments during back-propagation training which ultimately rendered the net rules incomprehensible. A new technique is now developed that allows the neulonet to learn by composing the net rules using genetic programming without th

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KONTOPOULOS, EFSTRATIOS, NICK BASSILIADES, GRIGORIS ANTONIOU, and ANNA SERIDOU. "VISUAL MODELING OF DEFEASIBLE LOGIC RULES WITH DR-VisMo." International Journal on Artificial Intelligence Tools 17, no. 05 (2008): 903–24. http://dx.doi.org/10.1142/s0218213008004217.

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The standardization of the Semantic Web has reached as far as ontologies and ontology languages. However, in order for the full potential of the Semantic Web to be achieved, the ability of reasoning over the available information is also essential. Rules can assist in this affair and various logics have been proposed for the Semantic Web domain. One of them is defeasible reasoning that deals with incomplete and conflicting information. However, despite its solid mathematical notation, it may be confusing to end users. To confront this downside, we proposed a representation schema for defeasibl

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40

Shapiro, Stewart. "Second-Order Logic, Foundations, and Rules." Journal of Philosophy 87, no. 5 (1990): 234. http://dx.doi.org/10.2307/2026832.

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Rábová, Ivana. "The formal logic of business rules." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 55, no. 6 (2007): 133–40. http://dx.doi.org/10.11118/actaun200755060133.

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Identification of improvement areas and utilization of information and communication technologies have gained value and priority in our knowledge driven society. Rules define constraints, conditions and policies of how the business processes are to be performed but they also affect the behavior of the resource and facilitate strategic business goals achieving. They control the business and represent business knowledge. The research works about business rules show how to specify and classify business rules from the business perspective and to establish an approach to managing them that will ena

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Arioua, Abdallah, Madalina Croitoru, and Srdjan Vesic. "Logic-based argumentation with existential rules." International Journal of Approximate Reasoning 90 (November 2017): 76–106. http://dx.doi.org/10.1016/j.ijar.2017.07.004.

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Osborne, Carl A. "Golden rules to nurture nephrologic logic." Journal of the American Veterinary Medical Association 217, no. 11 (2000): 1622–24. http://dx.doi.org/10.2460/javma.2000.217.1622.

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Wong, K. "Sound and Complete Inference Rules for SE-Consequence." Journal of Artificial Intelligence Research 31 (January 31, 2008): 205–16. http://dx.doi.org/10.1613/jair.2472.

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The notion of strong equivalence on logic programs with answer set semantics gives rise to a consequence relation on logic program rules, called SE-consequence. We present a sound and complete set of inference rules for SE-consequence on disjunctive logic programs.

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Мучник, Б., and B. Muchnik. "A Case for Communicative Logic of Text as a Distinct Discipline." Scientific Research and Development. Modern Communication Studies 7, no. 2 (2018): 40–48. http://dx.doi.org/10.12737/article_5ab4dff6e6c207.59085737.

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We demonstrate that communicative logic of text exists objectively, is distinct from conventional logic and deserves dedicated study. In order to highlight the difference between the two logics we contrast the typical flaws addressed by them. Conventional logic: non sequitur, vicious circle, false premise, hasty generalisation, the post hoc fallacy. Communicative logic: superfluous information, unjustified omission, misplaced elements, structural ambiguity. A large-scale experimental study of perception of communicatively deficient texts allowed us to formulate a set of rules aimed at construc

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Nugroho, Rizky, Adila Krisnadhi, and Ari Saptawijaya. "Large Language Model-Based Extraction of Logic Rules from Technical Standards for Automatic Compliance Checking." Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) 9, no. 2 (2025): 343–56. https://doi.org/10.29207/resti.v9i2.6285.

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In this research, we design logic rules as a representation of technical standards documents related to ship design, which will be used in automatic compliance checking. We present a novel design of logic rules based on a general pattern of technical standards’ clauses that can be produced automatically from text using a large language model (LLM). We also present a method to extract said logic rules from text. First, we design data structures to represent the technical standards and logic rules used to process the data. Second, the representation of technical standards is produced manually an

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Sen, Prithviraj, Breno W. S. R. de Carvalho, Ryan Riegel, and Alexander Gray. "Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (2022): 8212–19. http://dx.doi.org/10.1609/aaai.v36i8.20795.

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Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned ``rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer a strong connection to class

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ALIZADEH, MAJID, FARZANEH DERAKHSHAN, and HIROAKIRA ONO. "UNIFORM INTERPOLATION IN SUBSTRUCTURAL LOGICS." Review of Symbolic Logic 7, no. 3 (2014): 455–83. http://dx.doi.org/10.1017/s175502031400015x.

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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 substru

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Došen, Kosta. "Sequent-systems for modal logic." Journal of Symbolic Logic 50, no. 1 (1985): 149–68. http://dx.doi.org/10.2307/2273797.

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AbstractThe purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 2 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right of level 2, which when applied to Thinning on the right of level 1 produces intuitionistic out of classical logic (

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XU, MAI, MARIA PETROU, and JIANHUA LU. "LEARNING LOGIC RULES FOR THE TOWER OF KNOWLEDGE USING MARKOV LOGIC NETWORKS." International Journal of Pattern Recognition and Artificial Intelligence 25, no. 06 (2011): 889–907. http://dx.doi.org/10.1142/s0218001411008610.

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In this paper, we propose a novel logic-rule learning approach for the Tower of Knowledge (ToK) architecture, based on Markov logic networks, for scene interpretation. This approach is in the spirit of the recently proposed Markov logic networks for machine learning. Its purpose is to learn the soft-constraint logic rules for labeling the components of a scene. In our approach, FOIL (First Order Inductive Learner) is applied to learn the logic rules for MLN and then gradient ascent search is utilized to compute weights attached to each rule for softening the rules. This approach also benefits

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