Utility Functions: A Compromise Programming Approach to Specification and Optimization

Nowadays, utility theory and compromise programming (CP) are considered very different paradigms and methodologies to measure preferences as well as to determine decision maker's optima on an efficient frontier. In this paper, however, we show that a utility function with separate variables (presented in the form of a Taylor series around the ideal point) is reducible to a weighted sum of CP distances. This linkage between utility and compromise (based on a main assumption in which the usual utility functions hold) leads to (i) a method for specification and optimization of usual utility functions by operational technique and (ii) a reformulation of standard CP with the advantage of determining the best CP solution from a utility perspective. © 1997 John Wiley & Sons, Ltd.     

Preference Structure Modelling for Multi-objective Decision Making: A Goal–Programming Approach

We propose a new approach for modelling preference structures in multi-objective decision-making (MODM) problems. The basic idea of the approach is to first develop PROMETHEE-influenced objective functions and then to use these to reformulate the problem as a distance-based goal–programming (GP) model. Three basic functional forms are proposed and explicit expressions are developed for them. Among other things, the expressions allow for the straightforward development of an interactive framework while keeping the information requirements from the decision maker (DM) at a minimum. An ‘automatic’ piecewise linear approximation scheme is proposed for solving the GP model. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 150–154 (1997) No. of Figures: 0. No. of Tables: 0. No. of References: 12.     

A computational analysis of general intelligence tests for evaluating cognitive development

The progression in several cognitive tests for the same subjects at different ages provides valuable information about their cognitive development. One question that has caught recent interest is whether the same approach can be used to assess the cognitive development of artificial systems. In particular, can we assess whether the ‘fluid’ or ‘crystallised’ intelligence of an artificial cognitive system is changing during its cognitive development as a result of acquiring more concepts? In this paper, we address several IQ tests problems (odd-one-out problems, Raven’s Progressive Matrices and Thurstone’s letter series) with a general learning system that is not particularly designed on purpose to solve intelligence tests. The goal is to better understand the role of the basic cognitive operational constructs (such as identity, difference, order, counting, logic, etc.) that are needed to solve these intelligence test problems and serve as a proof-of-concept for evaluation in other developmental problems. From here, we gain some insights into the characteristics and usefulness of these tests and how careful we need to be when applying human test problems to assess the abilities and cognitive development of robots and other artificial cognitive systems.     

Rule-based schema matching for ontology-based mediators

Mediating heterogeneous data sources heavily relies on explicit domain knowledge expressed, for example, as ontologies and mapping rules. We discuss the use of logic representations for mapping schema elements onto concepts expressed in a simplified ontology for cultural assets. Starting with a logic representation of the ontology, criteria for a rule-based schema matching are exemplified. Special requirements are the handling of uncertain information and the processing of hierarchical XML structures representing instances.     

Epistemology and artificial intelligence

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology approaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relations.     

An evolutionary system for neural logic networks using genetic programming and indirect encoding

Nowadays, intelligent connectionist systems such as artificial neural networks have been proved very powerful in a wide area of applications. Consequently, the ability to interpret their structure was always a desirable feature for experts. In this field, the neural logic networks (NLN) by their definition are able to represent complex human logic and provide knowledge discovery. However, under contemporary methodologies, the training of these networks may often result in non-comprehensible or poorly designed structures. In this work, we propose an evolutionary system that uses current advances in genetic programming that overcome these drawbacks and produces neural logic networks that can be arbitrarily connected and are easily interpretable into expert rules. To accomplish this task, we guide the genetic programming process using a context-free grammar and we encode indirectly the neural logic networks into the genetic programming individuals. We test the proposed system in two problems of medical diagnosis. Our results are examined both in terms of the solution interpretability that can lead in knowledge discovery, and in terms of the achieved accuracy. We draw conclusions about the effectiveness of the system and we propose further research directions.     

Logic programs and connectionist networks

One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic programs can be computed by feedforward connectionist networks, and that the same semantic operators for first-order normal logic programs can be approximated by feedforward connectionist networks. Turning the networks into recurrent ones allows one also to approximate the models associated with the semantic operators. Our methods depend on a well-known theorem of Funahashi, and necessitate the study of when Funahashi's theorem can be applied, and also the study of what means of approximation are appropriate and significant.     

Proof theory and mathematical meaning of paraconsistent C-systems

A proof-theoretic analysis and new arithmetical semantics are proposed for some paraconsistent C-systems, which are a relevant sub-class of Logics of Formal Inconsistency (LFIs) introduced by W.A. Carnielli et al. (2002, 2005) [8] and [9]. The sequent versions BC, CI, CIL of the systems bC, Ci, Cil presented in Carnielli et al. (2002, 2005) [8] and [9] are introduced and examined. BC, CI, CIL admit the cut-elimination property and, in general, a weakened sub-formula property. Moreover, a formal notion of constructive paraconsistent system is given, and the constructivity of CI is proven. Further possible developments of proof theory and provability logic of CI-based arithmetical systems are sketched, and a possible weakened Hilbert?s program is discussed. As to the semantical aspects, arithmetical semantics interprets C-system formulas into Provability Logic sentences of classical Arithmetic PA (Artemov and Beklemishev (2004) [2], Japaridze and de Jongh (1998) [19], Gentilini (1999) [15], Smorynski (1991) [22]): thus, it links the notion of truth to the notion of provability inside a classical environment. It makes true infinitely many contradictions B∧¬B and falsifies many arbitrarily complex instances of non-contradiction principle ¬(A∧¬A). Moreover, arithmetical models falsify both classical logic LK and intuitionistic logic LJ, so that a kind of metalogical completeness property of LFI-paraconsistent logic w.r.t. arithmetical semantics is proven. As a work in progress, the possibility to interpret CI-based paraconsistent Arithmetic PACI into Provability Logic of classical Arithmetic PA is discussed, showing the role that PACIarithmetical models could have in establishing new meta-mathematical properties, e.g. in breaking classical equivalences between consistency statements and reflection principles.     

Levels of modality for BDI Logic

The use of rational agents for modelling real world problems has both been heavily investigated and become well accepted, with BDI (Beliefs, Desires, and Intentions) Logic being a widely used architecture to represent and reason about rational agency. However, in the real world, we often have to deal with different levels of confidence in the beliefs we hold, desires we have, and intentions that we commit to. This paper extends our previous framework that integrated qualitative levels of beliefs, desires, and intentions into BDI Logic. We describe an expanded set of axioms and properties of the extended logic. We present a modular structure for the semantics which involves a non-normal Kripke type semantics that may be used for other agent systems. Further, we demonstrate the usefulness of our framework with a scheduling task example.     

Justification logics and hybrid logics

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less well known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here.