Abstract. The practice of first-order logic is replete with meta-level concepts. Most notably there are meta-variables ranging over formulae, variables, and terms, and properties of syntax such as alpha-equivalence, capture-avoiding substitution and assumptions about freshness of variables with respect to metavariables. We present one-and-a-halfth-order logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of one-and-a-halfth-order logic derivability, show them equivalent, show that the derivations satisfy cut-elimination, and prove correctness of an interpretation of first-order logic within it. We discuss the technicalities in a wider context as a case-study 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

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 policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

this paper I treat conditionals using material implication, ignoring the well-known 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 DRT-like 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...

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 IJCAI-99, 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...

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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 re-use 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...

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 them|their names|and from the information that we store in them|their 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.

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

Access-Limited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledge-base. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an access-limited 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 knowledge-base, rather than the size of the entire knowledge-base. Access-Limited 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 knowledge-base, 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 non-trivial 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

I present a computationally-based representation for indefinite noun phrases and anaphora that models their use in natural language. To this end, three goals for knowledge representation for natural language processing: natural form, conceptual completeness, and structure sharing are described. In addressing these goals, an augmentation to the representation of variables (corresponding to indefinite noun phrases or anaphora) so that variables are not atomic terms is suggested. This leads to an extended, more "natural" representation. It is shown how this representation resolves some representational difficulties with sentences with nonlinear quantifier scoping, in particular, donkey sentences. 1 Introduction The intent of the work in this paper is to present a computationally-based representation for indefinite noun phrases and anaphora that models their use in natural language. To this end, I believe the following natural-language-specific goals must be addressed. First, the mapping ...