Systematic Verification of the Modal Logic Cube in Isabelle/HOL

We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without restriction to the modal logic cube, and using encodings in first-order logic in combination with first-order automated theorem provers. In contrast, our solution is more elegant, transparent and effective. It employs an embedding of quantified modal logic in classical higher-order logic. Automated reasoning tools, such as Sledgehammer with LEO-II, Satallax and CVC4, Metis and Nitpick, are employed to achieve full automation. Though successful, the experiments also motivate some technical improvements in the Isabelle/HOL tool.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

SAT-based Explicit LTL Reasoning

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly outperforms all existing LTL satisfiability solvers. Furthermore, we show that the framework can be extended from propositional LTL to assertional LTL (where we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and demonstrating that this can yield an exponential improvement in performance

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

The Noetic Account of Scientific Progress and the Factivity of Understanding

There are three main accounts of scientific progress: 1) the epistemic account, according to which an episode in science constitutes progress when there is an increase in knowledge; 2) the semantic account, according to which progress is made when the number of truths increases; 3) the problem-solving account, according to which progress is made when the number of problems that we are able to solve increases. Each of these accounts has received several criticisms in the last decades. Nevertheless, some authors think that the epistemic account is to be preferred if one takes a realist stance. Recently, Dellsén proposed the noetic account, according to which an episode in science constitutes progress when scientists achieve increased understanding of a phenomenon. Dellsén claims that the noetic account is a more adequate realist account of scientific progress than the epistemic account. This paper aims precisely at assessing whether the noetic account is a more adequate realist account of progress than the epistemic account

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition

Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo

Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models