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41
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 183 (21 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
Direct and Indirect Effects
, 2005
"... The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This pape ..."
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Cited by 76 (22 self)
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The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policyrelated interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends pathanalytic techniques to nonlinear and nonparametric models.
Choice Functions and the Scopal Semantics of Indefinites
 Linguistics and Philosophy
, 1997
"... this paper I treat conditionals using material implication, ignoring the wellknown semantic/pragmatic problems concerning their correct interpretation. Of course, one may doubt whether (7a), which is verified by any situation in which there is one woman who did not come to the party, reflects corre ..."
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Cited by 48 (12 self)
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this paper I treat conditionals using material implication, ignoring the wellknown semantic/pragmatic problems concerning their correct interpretation. Of course, one may doubt whether (7a), which is verified by any situation in which there is one woman who did not come to the party, reflects correctly the wide scope reading of the indefinite in (7). Obviously, this problem is independent of the scope problem of indefinites. For this reason and because antecedents of conditionals are one of the simplest and most striking cases of scope islands, I use such examples freely, counting on the reader to substitute her favorite theory of conditionals for material implication. This claim has been challenged in Farkas (1981), Rooth & Partee (1982:fn.6) and, more recently, in Ruys (1992) and Abusch (1994). These works all show cases where Fodor & Sag's claim is argued to be incorrect. The empirical debate will be reviewed later in this paper (subsection 3.4.2). Ruys and Abusch both conclude that Fodor & Sag's "referential" approach is inadequate. To handle the facts, Ruys proposes an indexing mechanism of indefinites within a DRTlike interpretation of LF. Abusch proposes to enrich DRT with a storage mechanism that changes the syntactic position of the N' predicate (= the restriction of the indefinite) at the representational level. Both Ruys and Abusch therefore accept the assumption of DRT about a distinct syntactic representational level for meaning. This level (sometimes called Logical Form') is additional to the syntactic level that undergoes semantic interpretation (GB's Logical Form, other theories' Surface Structure). Indefinites in Ruys and Abusch's treatments are not quantifiers. Instead, they involve the familiar treatment of DRT using free variables. I henceforth c...
Reasoning With Cause And Effect
, 1999
"... This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI99, and is intended to supplement the lecture with technical details and pointers to mo ..."
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Cited by 36 (0 self)
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This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...
Natural Language Processing Using a Propositional Semantic Network with Structured Variables
 Minds and Machines
, 1993
"... We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structured terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this le ..."
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Cited by 28 (12 self)
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We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structured terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this leads to an extended, more "natural" formalism whose use and representations are consistent with the use of variables in natural language in two ways: the structure of representations mirrors the structure of the language and allows reuse phenomena such as pronouns and ellipsis. Second, the formalism allows the specification of description subsumption as a partial ordering on related concepts (variable nodes in a semantic network) that relates more general concepts to more specific instances of that concept, as is done in language. Finally, this structured variable representation simplifies the resolution of some representational difficulties with certain classes of natural language sentences...
Merging without mystery, variables in dynamic semantics
, 1993
"... In this paper we discuss the treatment ofvariables in dynamic semantics. Referent systems are introduced as a exible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which wemanipulate themtheir namesand from th ..."
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Cited by 26 (0 self)
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In this paper we discuss the treatment ofvariables in dynamic semantics. Referent systems are introduced as a exible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which wemanipulate themtheir namesand from the information that we store in themtheir values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with the familiar formalisms in dynamic semantics, DRT and DPL.
AccessLimited Logic  A language for knowledgerepresentation
, 1990
"... AccessLimited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves all ..."
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Cited by 16 (3 self)
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AccessLimited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves all assertions reachable by following an available access path. The time complexity of inference is thus a polynomial function of the size of the accessible portion of the knowledgebase, rather than the size of the entire knowledgebase. AccessLimited Logic, though incomplete, still has a well defined semantics and a weakened form of completeness, Socratic Completeness, which guarantees that for any query which is a logical consequence of the knowledgebase, there exists a series of queries after which the original query will succeed. We have implemented ALL in Lisp and it has been used to build several nontrivial systems, including versions of Qualitative Process Theory and Pearl's probability networks. ALL is a step toward providing the properties clean semantics, efficient inference, expressive power which will be necessary to build large, effective knowledge
Characteristica Universalis
 Language, Truth and Ontology
, 1990
"... iments made upon diagrams. The latter are 'questions put to the [48] Nature of the relations concerned'  precisely in virtue of the fact that we are here experimenting with diagrams which are to enjoy the property that the forms of relations exemplified in reality will be the very same as the forms ..."
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Cited by 16 (10 self)
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iments made upon diagrams. The latter are 'questions put to the [48] Nature of the relations concerned'  precisely in virtue of the fact that we are here experimenting with diagrams which are to enjoy the property that the forms of relations exemplified in reality will be the very same as the forms of relations in the diagrams themselves. A similar idea is of course present also in Wittgenstein. As the Tractatus has it: 'What constitutes a picture is that its elements are related to one another in a determinate way.' (2.41 ) Indeed:' There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all.' (2.16) Wittgenstein's 'pictorial form', then, is Peirce's 'form of a relation', and our task here will be one of taking further the idea of a universal characteristic which both philosophers shared. 2. From Leibniz to Frege The project of such a characteristic had of course been envisaged by Leibniz, and the idea is present already