We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers # new and # new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predic...

Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higher-level belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.

According to the logical model of Information Retrieval (IR), the task of IR can be described as the extraction, from a given document base, of those documents d that, given a query q, make the formula d → q valid, where d and q are formulae of the chosen logic and “→ ” denotes the brand of logical implication formalized by the logic in question. In this paper, although essentially subscribing to this view, we propose that the logic to be chosen for this endeavour be a Terminological Logic (TL): accordingly, the IR task becomes that of singling out those documents d such that d � q, where d and q are terms of the chosen TL and “�” denotes subsumption between terms. We call this the terminological model of IR. TLs are particularly suitable for modelling IR; in fact, they can be employed: 1) in representing documents under a variety of aspects (e.g. structural, layout, semantic content); 2) in representing queries; 3) in representing lexical, “thesaural ” knowledge. The fact that a single logical language can be used for all these representational endeavours ensures that all these sources of knowledge will participate in the retrieval process in a uniform and principled way. In this paper we introduce Mirtl, a TL for modelling IR according to the above guidelines; its syntax, formal semantics and inferential algorithm are described. 1

Problems in logic are well-known to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically well-founded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...

Hybrid inference systems are an important way to address the fact that intelligent systems have muiltifaceted representational and reasoning competence. KRYPTON is an experimental prototype that competently handles both terminological and assertional knowledge; these two kinds of information are tightly linked by having sentences in an assertional component be formed using structured complex predicates denned in a complementary terminological component. KRYPTON is unique in that it combines in a completely integrated fashion a frame-based description language and a first-order resolution theorem-prover. We give here both a formal Knowledge Level view of the user interface to KRYPTON and the technical Symbol Level details of the integration of the two disparate components, thus providing an essential picture of the abstract function that KRYPTON computes and the implementation technology needed to make it work. We also illustrate the kind of complex question the system can answer. I

We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1

Abstract. Research on multimedia information retrieval (MIR) has recently witnessed a booming interest. A prominent feature of this research trend is its simultaneous but independent materialization within several fields of computer science. The resulting richness of paradigms, methods and systems may, on the long run, result in a fragmentation of efforts and slow down progress. The primary goal of this study is to promote an integration of methods and techniques for MIR by contributing a conceptual model that encompasses in a unified and coherent perspective the many efforts that are being produced under the label of MIR. The model offers a retrieval capability that spans two media, text and images, but also several dimensions: form, content and structure. In this way, it reconciles similarity-based methods with semantics-based ones, providing the guidelines for the design of systems that are able to provide a generalized multimedia retrieval service, in which the existing forms of retrieval not only coexist, but can be combined in any desired manner. The model is formulated in terms of a fuzzy description logic, which plays a twofold role: (1) it directly models semantics-based retrieval, and (2) it offers an ideal framework for the integration of the multimedia and multidimensional aspects of retrieval mentioned above. The model also accounts for relevance feedback in both text and image retrieval, integrating known techniques for taking into account user judgments. The implementation of

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Law of Residuation (in their j-th place) when f and g are contrapositives (with respect to their j-th place) and S(f; a 1 ; : : : ; a j ; : : : ; a n ; b) iff S(g; a 1 ; : : : ; b; : : : ; a n ; a j ). (5) Two operators f , g 2 OP are relatives when they satisfy the Abstract Law of Residuation in some position. (6) The family of operations OP is founded when there is a distinguished operator f 2 OP (the head) such that any other operator g 2 OP is a relative of f . Definition. A partial-gaggle is a tonoid T = (X; ; OP), in which OP is a founded family. As examples, consider a p.o. residuated groupoid, with OP chosen to be any of the following families of operations (ffi is the head of the families of which it is a member): fffig, fffi; /g, fffi; !g, fffi; /;!g, f/g, f!g. Note that f!;/g does not formally fall under our definition since the trace of one is not directly the contrapositive of the trace of the other, even though the trace of each is a contrapositive of the trace of f...

A Terminological Logic is presented as an information retrieval model, with a four-valued semantics that gives to its inference relation the flavour of relevance, that is a strict connection in meaning between the premises and the conclusion of the arguments licensed by the logic. The logic also permits the expression of meta-knowledge enforcing a closed-world reading of the knowledge concerning specified individuals and primitive concepts. A Gentzen-style, sound and complete calculus for reasoning in the logic is given, thus establishing the basis for an information retrieval engine.