Applications of Nonclassical Logic Methods for Purposes of Knowledge Discovery and Data Mining

* The work is partially supported by Grant no. NIP917 of the Ministry of Science and Education – Republic of Bulgaria.

Representing "Recursive" Default Logic in Modal Logic

The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults.

On the Relationships Among Quantified Autoepistemic Logic, its Kernel, and Quantified Reflective Logic

A Quantified Autoepistemic Logic is axiomatized in a monotonic Modal Quantificational Logic whose modal laws are slightly stronger than S5. This Quantified Autoepistemic Logic obeys all the laws of First Order Logic and its L predicate obeys the laws of S5 Modal Logic in every fixed-point. It is proven that this Logic has a kernel not containing L such that L holds for a sentence if and only if that sentence is in the kernel. This result is important because it shows that L is superfluous thereby allowing the ori ginal equivalence to be simplified by eliminating L from it. It is also shown that the Kernel of Quantified Autoepistemic Logic is a generalization of Quantified Reflective Logic, which coincides with it in the propositional case.

Systems Analysis: the Structure-and-Purpose Approach Based on Logic-linguistic Formalisation

Systems analysis (SA) is widely used in complex and vague problem solving. Initial stages of SA are analysis of problems and purposes to obtain problems/purposes of smaller complexity and vagueness that are combined into hierarchical structures of problems(SP)/purposes(PS). Managers have to be sure the PS and the purpose realizing system (PRS) that can achieve the PS-purposes are adequate to the problem to be solved. However, usually SP/PS are not substantiated well enough, because their development is based on a collective expertise in which logic of natural language and expert estimation methods are used. That is why scientific foundations of SA are not supposed to have been completely formed. The structure-and-purpose approach to SA based on a logic-and-linguistic simulation of problems/purposes analysis is a step towards formalization of the initial stages of SA to improve adequacy of their results, and also towards increasing quality of SA as a whole. Managers of industrial organizing systems using the approach eliminate logical errors in SP/PS at early stages of planning and so they will be able to find better decisions of complex and vague problems.

Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold.

Representing Default Logic in Modal Logic

The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan Formula and its converse hold.

On the Relationship between Quantified Reflective Logic and Quantified Default Logic

Reflective Logic and Default Logic are both generalized so as to allow universally quantified variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are then compared by deriving metatheorems of Z that express their relationships. The main result is to show that every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and Quantified Default Logic have exactly the same solutions when no default has an entailment condition.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

Application of Fuzzy Logic on Image Edge Detection

In this paper a novel method for an application of digital image processing, Edge Detection is developed. The contemporary Fuzzy logic, a key concept of artificial intelligence helps to implement the fuzzy relative pixel value algorithms and helps to find and highlight all the edges associated with an image by checking the relative pixel values and thus provides an algorithm to abridge the concepts of digital image processing and artificial intelligence. Exhaustive scanning of an image using the windowing technique takes place which is subjected to a set of fuzzy conditions for the comparison of pixel values with adjacent pixels to check the pixel magnitude gradient in the window. After the testing of fuzzy conditions the appropriate values are allocated to the pixels in the window under testing to provide an image highlighted with all the associated edges.

Misrepresentations and flawed logic about the prevalence of false memories

Brewin and Andrews (2016) propose that just 15% of people, or even fewer, are susceptible to false childhood memories. If this figure were true, then false memories would still be a serious problem. But the figure is higher than 15%. False memories occur even after a few short and low-pressure interviews, and with each successive interview they become richer, more compelling, and more likely to occur. It is therefore dangerously misleading to claim that the scientific data provide an “upper bound” on susceptibility to memory errors. We also raise concerns about the peer review process.

A kínai reformfolyamat politikai gazdaságtani logikája (The politico-economic logic of the Chinese reform process)

Kína az elmúlt több mint három évtizedben szegény, elmaradott országból a világgazdaság egyik legfontosabb szereplője lett. Szocialista rendszerét egy sajátos kapitalista rendszer váltotta fel, miközben politikai struktúrája lényegében változatlan maradt. A folyamatok során a vezetés mindvégig ügyelt arra, hogy a kommunista párt egyeduralmát semmi se veszélyeztethesse, ugyanakkor megfelelő források álljanak rendelkezésre hatalma megtartásához. A tanulmány a kínai reformfolyamatot politikai gazdaságtani szempontból vizsgálja, különös figyelmet szentelve az intézményi változásoknak. Bemutatja, milyen okok és tényezők álltak a reformok elindításának hátterében, milyen változások következtek be a szereplők érdekviszonyaiban a reformok előrehaladtával, és mire lehet számítani a reformok jövőjét illetően. Úgy tűnik, hogy a jelenlegi rendszer érdekviszonyai a reformok folytatása ellen hatnak, ellehetetlenítve a piacgazdaság intézményrendszerének további kiépítését. A járadékok és privilégiumok az elitet abban sem teszik érdekeltté, hogy komolyabb politikai reformokat hajtson végre, így a kialakuló csapdahelyzet megakadályozza az átmenet kiteljesedését. ____ In the last three decades China has risen from being a poor and underdeveloped country to being one of the most important players in the world economy. Its planned economy has been replaced by a capitalist system, but its political structure has remained essentially unchanged. The leaders during the reform process have sought constantly to avert dangers to the rule of the Communist Party and gain access to valuable resources that allow power to be retained. The study approaches the Chinese reform process from a politico-economic point of view, focusing primarily on institutional changes. It reveals the main factors behind the various phases of reform, the constantly changing interests of the players, and the possible future of the process. It seems that under the current authoritarian regime, there are vested interests working against a continuation of the reforms and precluding full establishment of the institutional framework of a market economy. The elite is also deterred from implementing serious political reforms by the current rents and privileges. This leads to a trap that prevents completion of the transition process.

Pavement performance prediction using adaptive logic networks

Pavement performance is one of the most important components of the pavement management system. Prediction of the future performance of a pavement section is important in programming maintenance and rehabilitation needs. Models for predicting pavement performance have been developed on the basis of traffic and age. The purpose of this research is to extend the use of a relatively new approach to performance prediction in pavement performance modeling using adaptive logic networks (ALN). Adaptive logic networks have recently emerged as an effective alternative to artificial neural networks for machine learning tasks. ^ The ALN predictive methodology is applicable to a wide variety of contexts including prediction of roughness based indices, composite rating indices and/or individual pavement distresses. The ALN program requires key information about a pavement section, including the current distress indexes, pavement age, climate region, traffic and other variables to predict yearly performance values into the future. ^ This research investigates the effect of different learning rates of the ALN in pavement performance modeling. It can be used at both the network and project level for predicting the long term performance of a road network. Results indicate that the ALN approach is well suited for pavement performance prediction modeling and shows a significant improvement over the results obtained from other artificial intelligence approaches. ^

An automatic tuning strategy for local fuzzy logic ramp metering algorithm using Particle Swarm Optimization (PSO)

Freeway systems are becoming more congested each day. One contribution to freeway traffic congestion comprises platoons of on-ramp traffic merging into freeway mainlines. As a relatively low-cost countermeasure to the problem, ramp meters are being deployed in both directions of an 11-mile section of I-95 in Miami-Dade County, Florida. The local Fuzzy Logic (FL) ramp metering algorithm implemented in Seattle, Washington, has been selected for deployment. The FL ramp metering algorithm is powered by the Fuzzy Logic Controller (FLC). The FLC depends on a series of parameters that can significantly alter the behavior of the controller, thus affecting the performance of ramp meters. However, the most suitable values for these parameters are often difficult to determine, as they vary with current traffic conditions. Thus, for optimum performance, the parameter values must be fine-tuned. This research presents a new method of fine tuning the FLC parameters using Particle Swarm Optimization (PSO). PSO attempts to optimize several important parameters of the FLC. The objective function of the optimization model incorporates the METANET macroscopic traffic flow model to minimize delay time, subject to the constraints of reasonable ranges of ramp metering rates and FLC parameters. To further improve the performance, a short-term traffic forecasting module using a discrete Kalman filter was incorporated to predict the downstream freeway mainline occupancy. This helps to detect the presence of downstream bottlenecks. The CORSIM microscopic simulation model was selected as the platform to evaluate the performance of the proposed PSO tuning strategy. The ramp-metering algorithm incorporating the tuning strategy was implemented using CORSIM's run-time extension (RTE) and was tested on the aforementioned I-95 corridor. The performance of the FLC with PSO tuning was compared with the performance of the existing FLC without PSO tuning. The results show that the FLC with PSO tuning outperforms the existing FL metering, fixed-time metering, and existing conditions without metering in terms of total travel time savings, average speed, and system-wide throughput.

On the Equivalence between Assumption-Based Argumentation and Logic Programming

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