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22
From inheritance relation to nonaxiomatic logic
 International Journal of Approximate Reasoning
, 1994
"... NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intensi ..."
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Cited by 33 (25 self)
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NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a NonAxiomatic Logic is de ned. It has a termoriented language and an experiencegrounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.
Nonaxiomatic reasoning system (version 2.2
, 1993
"... NonAxiomatic Reasoning System (NARS) is an intelligent reasoning system, where intelligence means working and adapting with insu cient knowledge and resources. NARS uses a new form of term logic, or an extended syllogism, in which several types of uncertainties can be represented and processed, and ..."
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Cited by 13 (11 self)
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NonAxiomatic Reasoning System (NARS) is an intelligent reasoning system, where intelligence means working and adapting with insu cient knowledge and resources. NARS uses a new form of term logic, or an extended syllogism, in which several types of uncertainties can be represented and processed, and in which deduction, induction, abduction, and revision are carried out in a uni ed format. The system works in an asynchronously parallel way. The memory of the system is dynamically organized, and can also be interpreted as a network. After present the major components of the system, its implementation is brie y described. An example is used to show howthe system works. The limitations of the system are also discussed. 1
Combining Derivations and Refutations for Cutfree Completeness in BiIntuitionistic Logic
, 2008
"... Biintuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cutfree ” sequent calculus has recently been shown to fail cutelimination. We present a new cutfree se ..."
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Cited by 7 (0 self)
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Biintuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cutfree ” sequent calculus has recently been shown to fail cutelimination. We present a new cutfree sequent calculus for biintuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and past modalities in tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose. 1
A Sequent Calculus for Skeptical Default Logic
 Proc. of the Int. Conf. on Automated Reasoning with Analytic Tableaux and Related Methods, SpringerVerlag LNCS 1227
, 1997
"... . In this paper, we contribute to the prooftheory of Reiter's Default Logic by introducing a sequent calculus for skeptical reasoning. The main features of this calculus are simplicity and regularity, and the fact that proofs can be surprisingly concise and, in many cases, involve only a small ..."
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Cited by 7 (1 self)
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. In this paper, we contribute to the prooftheory of Reiter's Default Logic by introducing a sequent calculus for skeptical reasoning. The main features of this calculus are simplicity and regularity, and the fact that proofs can be surprisingly concise and, in many cases, involve only a small part of the default theory. 1 Introduction Nonmonotonic logics play a fundamental role in knowledge representation and commonsense reasoning, as well as in the theory of programming languages. 1 The semantic and algorithmic aspects of nonmonotonic reasoning have been extensively investigated (e.g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the prooftheoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention on general properties of nonmonotonic inference, rather than on specific formalisms. In particular, they do not axio...
An Aristotelian Understanding of ObjectOriented Programming
 In Proceedings of the conference on Objectoriented programming, systems, languages, and applications
, 2000
"... The folklore of the objectoriented programming community at times maintains that objectoriented programming has drawn inspiration from philosophy, specifically that of Aristotle. We investigate this relation, first of all, in the hope of attaining a better understanding of objectoriented programm ..."
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Cited by 5 (1 self)
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The folklore of the objectoriented programming community at times maintains that objectoriented programming has drawn inspiration from philosophy, specifically that of Aristotle. We investigate this relation, first of all, in the hope of attaining a better understanding of objectoriented programming and, secondly, to explain aspects of Aristotelian logic to the computer science research community (since it differs from first order predicate calculus in a number of important ways). In both respects we endeavour to contribute to the theory of objects, albeit in a more philosophical than mathematical fashion.
Some Thoughts on Mohist Logic
"... ABSTRACT. The paper is an exploration of the old Chinese texts called the the Mohist Canons from a modern logical perspective. We explain what the Mohists have contributed to logic, while we also provide some new interpretations of the issues discussed in the Canons. 1 ..."
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Cited by 5 (0 self)
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ABSTRACT. The paper is an exploration of the old Chinese texts called the the Mohist Canons from a modern logical perspective. We explain what the Mohists have contributed to logic, while we also provide some new interpretations of the issues discussed in the Canons. 1
On the Syllogistic Structure of ObjectOriented Programming
 In Hausi Müller, MaryJean Harrold, and Willhelm Shäfer, editors, ICSE’01
, 2001
"... Recent works by Sowa and by Rayside & Campbell demonstrate that there is a strong connection between objectoriented programming and the logical formalism of the syllogism, rst set down by Aristotle in the Prior Analytics. In this paper, we develop an understanding of polymorphic method invocations i ..."
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Cited by 4 (2 self)
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Recent works by Sowa and by Rayside & Campbell demonstrate that there is a strong connection between objectoriented programming and the logical formalism of the syllogism, rst set down by Aristotle in the Prior Analytics. In this paper, we develop an understanding of polymorphic method invocations in terms of the syllogism, and apply this understanding to the design of a novel editor for objectoriented programs. This editor is able to display a polymorphic call graph, which is a substantially more dif cult problem than displaying a nonpolymorphic call graph. We also explore the design space of program analyses related to the syllogism, and nd that this space includes Unique Name, Class
Proving unprovability in some normal modal logics
 Bulletin of the Section of Logic. Polish Academy of Science
, 1991
"... The present communication suggests deductive systems for the operator ⊣ of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of ̷Lukasiewicz: for every formula φ either ⊢ φ or ⊣ φ (but not both) is deriva ..."
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Cited by 3 (0 self)
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The present communication suggests deductive systems for the operator ⊣ of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of ̷Lukasiewicz: for every formula φ either ⊢ φ or ⊣ φ (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations. All background in modal logic, necessary for this paper can be found in the initial chapters of [1], [3] or [5]. Henceforth we shall informally read S ⊣ φ as “φ is unprovable in S”. All systems presented here will contain the “minimal ” ⊣ ⊢ system ̷L consisting of the axiom: F: ⊣ ⊥ and the rules:
Complementary logics for classical propositional languages. Kriterion. Zeitschrift fur Philosophie
, 1992
"... This note presents a simple axiomatic system by means of which exactly those sentences can be derived that are rated nontautologous in classical propositional logic. Since the logic is decidable, there exist of course many algorithms that do the job, e.g. using semantic tableaux or refutation trees ..."
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Cited by 3 (1 self)
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This note presents a simple axiomatic system by means of which exactly those sentences can be derived that are rated nontautologous in classical propositional logic. Since the logic is decidable, there exist of course many algorithms that do the job, e.g. using semantic tableaux or refutation trees. However, a formulation in terms of axioms and rules of inference is by no means a straightforward task, as these must be of a most nonstandard nonclassical sort. 1 For instance, axioms cannot be axiom schemata and standard substitution rules cannot hold, since a nontautology may well become tautologous upon substitution. Moreover, the system must be paraconsistent, i.e. such as to allow derivation of sentences with opposite truth values. The system presented here provides, I think, a rather nice way of dealing with these difficulties. Since tautologous sentences are also axiomatizable, the outcome is an exhaustive characterization of the logic of classical propositional languages in purely syntactic terms. The picture can then be completed by developing related systems axiomatizing classical contradictions, contingencies, noncontradictions
Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations (Extended Abstract)
"... Entailment relations are of central importance in the enterprise of natural language semantics. In modern logic, entailment relations are characterized from two viewpoints: the modeltheoretic and prooftheoretic ones. By contrast, most approaches to formalizing entailment relations in natural langua ..."
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Cited by 2 (1 self)
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Entailment relations are of central importance in the enterprise of natural language semantics. In modern logic, entailment relations are characterized from two viewpoints: the modeltheoretic and prooftheoretic ones. By contrast, most approaches to formalizing entailment relations in natural languages have been solely based on modeltheoretic conceptions. Thus,