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Experiments in automated deduction with condensed detachment
 in Proceedings of the Eleventh International Conference on Automated Deduction (CADE11), Lecture Notes in Artificial Intelligence
, 1992
"... This paper contains the results of experiments with several search strategies on 112 problems involving condensed detachment. The problems are taken from nine di erent logic calculi: three versions of the twovalued sentential calculus, the manyvalued sentential calculus, the implicational calculus ..."
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Cited by 24 (8 self)
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This paper contains the results of experiments with several search strategies on 112 problems involving condensed detachment. The problems are taken from nine di erent logic calculi: three versions of the twovalued sentential calculus, the manyvalued sentential calculus, the implicational calculus, the equivalential calculus, the R calculus, the left group calculus, and the right group calculus. Each problem was given to the theorem prover Otter and was run with at least three strategies: (1) a basic strategy, (2) a strategy with a more re ned method for selecting clauses on which to focus, and (3) a strategy that uses the re ned selection mechanism and deletes deduced formulas according to some simple rules. Two new features of Otter are also presented: the re ned method for selecting the next formula on which to focus, and a method for controlling memory usage. 1
The Shortest Single Axioms for Groups of Exponent 4
 Computers and Mathematics with Applications
, 1993
"... We study equations of the form (ff = x) which are single axioms for groups of exponent 4, where ff is a term in product only. Every such ff must have at least 9 variable occurrences, and there are exactly three such ff of this size, up to variable renaming and mirroring. These terms were found by an ..."
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Cited by 7 (2 self)
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We study equations of the form (ff = x) which are single axioms for groups of exponent 4, where ff is a term in product only. Every such ff must have at least 9 variable occurrences, and there are exactly three such ff of this size, up to variable renaming and mirroring. These terms were found by an exhaustive search through all terms of this form. Automated techniques were used in two ways: to eliminate many ff by verifying that (ff = x) true in some nongroup, and to verify that the group axioms do indeed follow from the successful (ff = x). We also present an improvement on Neumann's scheme for single axioms for varieties of groups. x0. Introduction. If n 1 is an integer, a group of exponent n is a group in which x n is the identity for all elements x. We study equations of the form (ff = x) which are single axioms for groups of exponent n, where ff is a term in product only. Note that in our definition of "exponent n", we do not require that n is the smallest exponent, so, for ...
Automated discovery of single axioms for ortholattices
 Algebra Universalis
, 2005
"... Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complemen ..."
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Cited by 4 (1 self)
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Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complementation. Proofs are omitted but are available in an associated technical report and on the Web. We used computers extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. 1.
Natural logic for natural language
 Lecture Notes in Computer Science, Volume 4363
, 2007
"... Abstract. For a cognitive account of reasoning it is useful to factor out the syntactic aspect — the aspect that has to do with pattern matching and simple substitution — from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of ap ..."
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Abstract. For a cognitive account of reasoning it is useful to factor out the syntactic aspect — the aspect that has to do with pattern matching and simple substitution — from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of appropriate substitutions at marked positions in syntactic structures. We first introduce the semantic and the syntactic sides of monotonicity reasoning or ‘natural logic’, and propose an improvement to the syntactic monotonicity calculus, in the form of an improved algorithm for monotonicity marking. Next, we focus on the role of monotonicity in syllogistic reasoning. In particular, we show how the syllogistic inference rules (for traditional syllogistics, but also for a broader class of quantifiers) can be decomposed in a monotonicity component, an argument swap component, and an existential import component. Finally, we connect the decomposition of syllogistics to the doctrine of distribution. 1
New foundations for imperative logic I: Logical connectives, consistency, and quantifiers
 Noûs
, 2008
"... Abstract. Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me ” is the conjunction of “kiss me ” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as th ..."
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Cited by 4 (4 self)
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Abstract. Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me ” is the conjunction of “kiss me ” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied⎯what more is there to say? Much more, I argue. “If you love me, kiss me”, a conditional imperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it is satisfied if you love and kiss me, violated if you love but don’t kiss me, and avoided if you don’t love me. So we need a logic of threevalued imperatives which mixes declaratives with imperatives. I develop such a logic. 1.
What does it mean to say that logic is formal
, 2000
"... Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and ..."
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topicneutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this
Short equational bases for ortholattices
 Preprint ANL/MCSP10870903, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL
, 2004
"... Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. ..."
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Cited by 3 (3 self)
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Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. Proofs are omitted but are available in an associated technical report. Computers were used extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. The notion of computer proof is addressed. 1
A Linguistic Analysis of Question Taxonomies
"... Recent work in automatic question answering has called for question taxonomies as a critical component of the process of machine understanding of questions. There is a long tradition of classifying questions in library reference services, and digital reference services have a strong need for automat ..."
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Recent work in automatic question answering has called for question taxonomies as a critical component of the process of machine understanding of questions. There is a long tradition of classifying questions in library reference services, and digital reference services have a strong need for automation to support scalability. Digital reference and question answering systems have the potential to arrive at a highly fruitful symbiosis. To move towards this goal, an extensive review was conducted of bodies of literature from several fields that deal with questions, to identify question taxonomies that exist in these bodies of literature. In the course of this review, five question taxonomies were identified, at four levels of linguistic analysis.
Summary
, 2008
"... This paper describes the main lines of the ‘natural logic ’ research program on direct reasoning with natural language in the 1980s done by the author and colleagues in the formal semantics community. It also identifies and discusses some main challenges to the program given what we know today. ..."
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This paper describes the main lines of the ‘natural logic ’ research program on direct reasoning with natural language in the 1980s done by the author and colleagues in the formal semantics community. It also identifies and discusses some main challenges to the program given what we know today.