3,349 research outputs found
Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis
Using the method of correspondence analysis, Tamminga obtains sound and complete natural deduction systems for all the unary and binary truth-functional extensions of Kleene’s strong three-valued logic K3 . In this paper, we extend Tamminga’s result by presenting an original finite, sound and complete proof-searching technique for all the truth-functional binary extensions of K3
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Normalisation for Some Quite Interesting Many-Valued Logics
In this paper, we consider a set of quite interesting three- and four-valued logics and prove the normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3⊃. Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation
The Logic of Internal Rational Agent
In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for . Finally, we formalize all the truth-functional -ary extensions of the negation fragment of (including itself) as well as their basic modal extension via linear-type natural deduction systems
The Logic of Internal Rational Agent
In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for . Finally, we formalize all the truth-functional -ary extensions of the negation fragment of (including itself) as well as their basic modal extension via linear-type natural deduction systems
Functional Completeness in CPL via Correspondence Analysis
Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The properties of soundness and completeness of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method.
Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness.Polish National Science Centre, grant no. 2017/26/E/HS1/00127Polish National Science Centre, grant no. 2017/25/B/HS1/0126
The Method of Socratic Proofs Meets Correspondence Analysis
The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs.
Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.Polish National Science Centre, grant no. 2017/26/E/HS1/00127Polish National
Science Centre, grant no. 2017/25/B/HS1/0126
Theoretical Engineering and Satellite Comlink of a PTVD-SHAM System
This paper focuses on super helical memory system's design, 'Engineering,
Architectural and Satellite Communications' as a theoretical approach of an
invention-model to 'store time-data'. The current release entails three
concepts: 1- an in-depth theoretical physics engineering of the chip including
its, 2- architectural concept based on VLSI methods, and 3- the time-data
versus data-time algorithm. The 'Parallel Time Varying & Data Super-helical
Access Memory' (PTVD-SHAM), possesses a waterfall effect in its architecture
dealing with the process of voltage output-switch into diverse logic and
quantum states described as 'Boolean logic & image-logic', respectively.
Quantum dot computational methods are explained by utilizing coiled carbon
nanotubes (CCNTs) and CNT field effect transistors (CNFETs) in the chip's
architecture. Quantum confinement, categorized quantum well substrate, and
B-field flux involvements are discussed in theory. Multi-access of coherent
sequences of 'qubit addressing' in any magnitude, gained as pre-defined, here
e.g., the 'big O notation' asymptotically confined into singularity while
possessing a magnitude of 'infinity' for the orientation of array displacement.
Gaussian curvature of k(k<0) is debated in aim of specifying the
2D electron gas characteristics, data storage system for defining short and
long time cycles for different CCNT diameters where space-time continuum is
folded by chance for the particle. Precise pre/post data timing for, e.g.,
seismic waves before earthquake mantle-reach event occurrence, including time
varying self-clocking devices in diverse geographic locations for radar systems
is illustrated in the Subsections of the paper. The theoretical fabrication
process, electromigration between chip's components is discussed as well.Comment: 50 pages, 10 figures (3 multi-figures), 2 tables. v.1: 1 postulate
entailing hypothetical ideas, design and model on future technological
advances of PTVD-SHAM. The results of the previous paper [arXiv:0707.1151v6],
are extended in order to prove some introductory conjectures in theoretical
engineering advanced to architectural analysi
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