Archive for the ‘Artificial Intelligence’ Category

Based on several years of research/thinking/lit review, I’ve come up with some opinions on the subject of logic et cetera. Since it’s mostly been myself talking to eccentric though lovable phil profs and a lot of old dead white men, I’d like to ask you, dear reader, for any thoughts or opinions on the final paragraph of mind-altering questions (the first few paragraphs intended to provide definitions and context):

Logic is defined here as the study of valid demonstration and inference, or the principles of correct reasoning. It concerns the structure of statements and arguments, and rules of inference in both formal systems and natural language. Formal logical systems consist of:

1. a formal language, and
2. a deductive system (or deductive apparatus) which consists of a set of inference rules and/or axioms.

Formal systems derive statements from prior statements in the system. A derived statement is called a theorem, whereas axioms are statements that are assumed to be true without proof (self-evidence).

Some of the desired properties possible for logical systems are: consistency (none of the system’s theorems contradict one another), soundness (the system’s rules of proof will never allow a false inference from a true premise), and completeness (that there are no true sentences in the system that cannot be proved in the system). Not all systems achieve all three virtues (e.g. Godel’s incompleteness theorems state no useful system of arithmetic can be both consistent and complete).

There are many types of logic – first-order logic, second-order logic, informal logic, interpretability logic, intuitionistic logic, quantum logic, categorical logic, clocked logic, linear logic, college logic, combinatorial logic, affine logic, Boolean logic, ternary logic, monotic logic, non-monotic logic, multivalued logic, paraconsistent logic, non-Aristotelian logic, relevant logic, temporal logic, sequential logic, scholastic logic, term logic — the list goes on. There are local and global logics, which hold different axioms or rules of inference. Despite its long history, the nature of logic is obscured by a number of disturbing questions that have yet to be satisfactorily answered.

Is there a single true logic, or are many logics equally correct? Is it possible to have genuine disagreements about the correctness of a logical principle? What makes a logical constant? What are the proper accounts of logical concepts (e.g. logical consequence, quantification, etc)? What is the scope of logic (e.g. does it encompass mathematics)? Is logic a matter of convention? What is the nature of logical necessity? What is the relationship between the verbal rules of logic and the mental ability to reason logically? Is logic subject to empirical revision?

Google Squared went live today! Instead of providing a list of links to ranked pages, Google Squared presents information derived from a query in a spreadsheet-like grid called a square.

“‘It essentially searches the Web to find the types of facts you might be interested in, extracts them and presents them in a meaningful way,” Google says. “If your square isn’t perfect at the beginning, it’s easy to work with Google Squared to get a better answer.”

This video, from Google’s blog, shows you some of the features.

Will Google Squared kill Wolfram Alpha?

“Google Squared is a search tool that helps you quickly build a collection of facts from the Web for any topic you specify:

* Facts about your topic are organized as a table of items and attributes (we call them “Squares” for fun).
* Customize these Squares to see just the items and attributes you’re interested in.
* See the websites that served as sources for the information in your Square.
* Save and share Squares with others.

“While gathering facts from across the Internet is relatively easy (albeit tedious) for humans to do, it’s far more difficult for computers to do automatically. Google Squared is a first step towards solving that challenge. It essentially searches the web to find the types of facts you might be interested in, extracts them and presents them in a meaningful way.”

Does this sound familiar?

Try searching for ‘roller coasters’ using Google Squared and Wolfram Alpha. The winner, here, is clear.

However, Wolfram Alpha can outperform Google at almost everything computational (can Google do this?).

Wolfram Alpha’s data was organized by real live humans; Google Squared is algorithmic.

In a way, this is a very interesting, very public example of the race between humans and machines; how long will it be before Google’s algorithms outstrip Wolfram Alpha’s literal brain-power. Can computers match our minds? Time will tell. Some certainly think so.

Wolfram Alpha has finally gone live, and I was eager to see if it lived up to the PR storm that preceded its launch. I still haven’t forgiven Wolfram for ANKOS, so I’ve  been pretty skeptical about W|A.

My first impression: Not bad. Not bad at all. It’s by far the best free online application I’ve seen for solving and graphing equations, so I’m going to be using it extensively for the rest of its lifetime. I’m interested to watch it grow in its ability to handle a wider variety of types of information. It’s fun to play with, even if it’s agonizingly slow on the day of its launch.

I tried things like:

• When is the next solar eclipse in Chicago, IL?
• Integrate digamma (d) dx from 6 to 10
• What is the answer to life, the universe, and everything?
• Melting point of gold in Kelvin
• Taylor series of (tan(x)^3)
• Who am I?
• Is there a God?
  
• How many angels can dance on the head of a pin?

It can handle roman numerals surprisingly well, and I may well stop paying for Mathematica (okay, I didn’t pay for mine). The graphs are beautiful, and feel very interactive. I doubt there are many questions related to math or the computational sciences that it can’t answer at least reasonably well (watch the wording, though).

Unfortunately, it couldn’t express miles in beardseconds, nor could it express Wolfram’s ego in milliDijkstras. However, overall, I think it’s off to a fantastic start. I wish I had it five years ago.

That’s it, lab techs. Pack up your things, and get your recommendation letters ready. Time to take your proper place on the sidelines, as a robot named Adam has made us all obsolete.

The Robot Scientist project at Aberystwyth University made headlines today, bringing us the first machine to have independently “discovered new scientific knowledge”.

Adam formulates hypotheses about the origins of “orphan enzymes” (enzymes we haven’t yet associated with their genes). The robot then plans and executes experiments to test its (his?) own hypotheses (!), selecting yeast mutants from a collection, incubating cells, and measuring their growth rates.

As the team reported this week in Science, Adam came up with 20 hypotheses about genes encoding 13 enzymes, 12 of which it confirmed. This tedious and time-consuming work will hopefully free up the schedules of scientists, who will be able to spend more time thinking about the results procured by these robots.

Team leader Ross King pointed out that his robotic associate is able to express scientific findings in a clearer way than humans. “It expresses its conclusions in logic,” he said. “Human language, with all its nuances, may not be the best way to communicate scientific findings.”

Their super-interesting manuscript, published in Science, can be accessed here.

For those of you subscription-less science-pirates, it can be accessed free here. Shh. Enjoy.