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304 pages

Foundations Without Foundationalism, A Case for Second-Order Logic

Creator: Stewart Shapiro | Mathematics - 2000-05-18

Foundations without Foundationalism is a key contribution both to philosophy of mathematics and to mathematical logic. 'In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics.

Publisher: Oxford University Press, USA

About this book
Stewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second-order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second-order andhigher-order logic, in a way that will be accessible to graduate students. He then demonstrates that second-order notions are prevalent in mathematics as practised, and that higher-order logic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical andhistorical issues that the subject raises. Foundations without Foundationalism is a key contribution both to philosophy of mathematics and to mathematical logic. 'In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics. His coverage of the wide range of logical and philosophical topics required for understanding the controversy over second-order logic is thorough, clear, and persuasive. . . .Shapiro recognizes that it is unlikely that he has had the last word on these controversial philosophical subjects. Nevertheless, his book is certainly an excellent place to start work on them.' Michael D. Resnik, History and Philosophy of Logic



626 pages

Computer Science Logic, 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Szeged, Hungary, September 25-29, 2006 : Proceedings

Creator: European Association for Computer Science Logic. Conference | 2006-11-13

The stable of the operators Da and Dt define the semantics of extensions (in )f default logic, proposed originally by Reiter, in the case of autoepis- ic the concept was not identified until algebraic considerations in [15] t).

Publisher: Springer Verlag

About this book
This book constitutes the refereed proceedings of the 20th International Workshop on Computer Science Logic, CSL 2006, held as the 15th Annual Conference of the EACSL in Szeged, Hungary in September 2006. The 37 revised full papers presented together with 4 invited contributions were carefully reviewed and selected from 132 submissions. All current aspects of logic in computer science are addressed, including automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and formal logics, modal and temporal logic, model checking, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, verification of security protocols, linear logic, higher-order logic, nonmonotonic reasoning, as well as logics and type systems for biology.



310 pages

Handbook of Philosophical Logic

Creator: Dov M. Gabbay | 2010-12-29

To understand what (K°3)-(K°5) say, two cases need to be considered: Case 1: KL) (p) is consistent. ... The particular way of writing the postulates given above makes use of technical properties of classical logic (the way inconsistent ...

Publisher: Springer-Verlag New York Incorporated

About this book
This book is indispensable to any advanced student or researcher using logic in these areas. The chapters are comprehensive and written by major figures in the field. Topics include, Belief Revision, Refutation Systems in Propositional Logic, Quantifier Scope in Formal Linguistics and Non-deterministic Semantics for Logical Systems.


Camera and Photo Accessories Directory

Case Logic - Camera Bags | Tablet Cases | Laptop Cases ...
At Case Logic we started out providing the best CD Cases & DVD Cases around. With so many electronics today we now offer protection for all devices including laptops ...

Logic - Wikipedia, the free encyclopedia
Logic (from the Ancient Greek: λογική, logike is the use and study of valid reasoning The study of logic features most prominently in the subjects of philosophy

Logic gate - Wikipedia, the free encyclopedia
In electronics, a logic gate is an idealized or physical device implementing a Boolean function ; that is, it performs a logical operation on one or more logical ...

Love and Logic - Helping Parents & Teachers Raise ...
Love and Logic provides help to parents, educators, teachers and facilitators. Techniques that help adults achieve respectful, healthy relationships with their ...

Conceptis logic puzzles - Have fun, get smart!
Nonstop fun with the world's best logic puzzles. Play new weekly puzzle games online, on your iPhone and iPad, or with pencil and paper.


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Editor's picks

  • Case Logic

    Case Logic PHDC-1 Compact Portable Hard Drive Case (Black)

    Personal Computer (Case Logic)

    Rating (0 reviews):
    (4.4/5)
    Case Logic

    Versatile and good quality

    I got this case in the blue color with a contrasting bright yellow interior. The material is all-around high-quality, and the case offers excellent protection for my external hard drive(s).Since this is a universal drive case it cannot be a perfect fit for every portable hard drive out there. I own several different-size drives and here is how they fit:- First generation WD Passport (silver colored, blueish rubberized bottom, ) fits perfectly. I suspect that this case was originally made for these drives.- Newer WD Passport (various colors, non-rubberized bottom, ... 4/5 I.Peters (Dallas, TX USA) - See all my reviews, April 16, 2008

    Good quality case, but a little too big for the Western Digital Passport drives

    0 4/5 B. Chiu "Spud" - See all my reviews, February 15, 2007

    Totally worth it!

    0 5/5 Claire Jordan "Filmmaker - "The Baroness ... (New Orleans, LA) - See all my reviews, May 7, 2010
    List Price: $69.99
    External Dimensions -5.5" x 3.75" x 1.25"
    Compact case to store or transport smaller portable hard drives
    Slimline design allows case to easily fit into any backpack or briefcase


  • Case Logic

    Case Logic KSW-320 Koskin 336 Capacity CD/DVD Prosleeves Wallet (Black)

    CE (Case Logic)
    List Price: $54.99
    Price: $27.77
    You Save: $27.22 (49%)

    Fast File holds an additional 16 CDs, use it to keep your favorite CDs easy to access
    Holds 320 CDs or 160 with liner notes
    Padded koskin exterior protects your CDs.


  • Case Logic

    Case Logic LAPS-113 13.3-Inch Laptop / MacBook Air / MacBook Pro Retina Display Sleeve (Black)

    Personal Computer (Case Logic)

    Rating (0 reviews):
    (4.3/5)
    Case Logic

    Fantastic Protective Sleeve For Macbook Pro's & Google Chrome Cr-48

    Case Logic, Inc. has been around since 1984, which is probably right about the time I bought my first Case Logic case for my cassette tapes. Over the years, as they added items to their product line, so I added their products to my collection. As a sample, I believe I have owned at one point or another, Case Logic cassette cases, CD & DVD cases, CD player cases, Zip Drive cases, trunk organizers, and more. I'm looking around my home office and I can spot several of their products and I bet you do too. Case Logic's 13.3 Laptop Sleeve (LAPS-113) is one of many sleeves that Case Logic makes and it just might be the perfect protective, no frills sleeve for your 13.3-inch or smaller laptop.PROS:- No nonsense, sleek design- 6mm EVA foam padding- Smooth gliding zipper- Protective lip prevents damage from zipperCONS:- Slight rubbery odorI define my perfect laptop sleeve to be one that has no handles, pockets, zippers, or bulk... 5/5 Ed (San Francisco Bay Area) - See all my reviews, March 1, 2011

    good little case

    0 4/5 Nicole Machi (Bass Lake, CA) - See all my reviews This review is from: Case Logic LAPS-113 13.3-Inch Laptop / MacBook Air / MacBook Pro Retina Display Sleeve (Red) (Personal Computers) I've been using this case a couple weeks and like it so far. I strongly recommend NOT BUYING THE RED ONE! I ordered it thinking black would be too boring but the red is not like the picture and its quite an ugly red.The case is soft with a few millimeters of foam. It isn't going to save your computer, but it will keep it from small scratches and dings while its being transported.I'd love a case that offered a bit of moisture protection, which this certainly does not, but for the price, it definitely meets my expectations. 0 Help other customers find the most helpful reviews  Was this review helpful to you? , June 19, 2012

    Sleek and secure

    I was expecting a mere utilitarian sleeve to hold my 13" Mac Pro laptop. I am delighted that it also provides some aesthetic satisfaction. The color is a solid inky black, with no lighter threads in the design. The Case Logic logo on the front is small, with the yellow-orange square of half-sun that pops out stylishly and yet is unobtrusive. The woven webbing on the sides is a nice nifty touch.The top-loading zipper--which is a primary feature for me in determining quality--is sturdy and smooth, and slides like buttah from one side to the other. It won't scratch your laptop because it has a protective lip. The 6 millimeter foam padding feels substantial and secure, and my laptop slips in easily, like a card in an envelope. It fits snugly but not too tightly, either.External dimensions are 14 x 1.1 x 10" and internal dimensions are 13 x 1.1 x 9.1" The exterior and lining is made of 100% polyester.The attached description card says "25 Years Quality... 5/5 "switterbug" Betsey Van Horn (Austin, Texas) - See all my reviews, April 8, 2011
    List Price: $29.99
    Product Dimensions (l x w x h): 14 x 1.1 x 10 in
    A seamless wrap of Impact Foam padding provides top to bottom protection
    Fits Devices (l x w x h): 13 x 1.1 x 9.1 in
    Slim-line design allows this case to be carried solo or fit in your favorite bag
    Woven webbing along each side adds subtle texture to the otherwise clean design
    Form-fitting sleeve ensures a precise fit for your laptop with a 13.3-Inch PC/MacBook display
    Quick top-loading access through envelope-style design


  • Case Logic

    Case Logic DLBP-116 16-Inch Laptop Backpack (Black)

    Personal Computer (Case Logic)
    List Price: $59.99

    A felt-like, scratch resistant pocket in the top is ideal for sunglasses or touch screen mobile phone
    Dedicated laptop compartment holds most laptops with up to a 16-Inch screen (compartment dimensions: 10.8 x 1.8 x 15.2-Inch)
    Zippered front pocket organizes your cell phone, MP3 player, cords and other accessories.
    Adjustable shoulder straps includes a strap management system to keep excess strap rolled up and out of the way
    Zippered pocket at the top of the pack is lined with a felt-like, scratch-resistant material that is ideal for sunglasses or touch screen devices


  • Case Logic

    Case Logic QHDC-101 Portable EVA Hard Drive Case - Black

    CE (Case Logic)
    List Price: $28.18
    Price: $7.51
    You Save: $20.67 (73%)

    Slimline design allows case to easily fit into any backpack or briefcase
    EVA Molded, Durable, semi-rigid exterior to protect valuable data
    Interior strap and zippered closure secures portable hard drive in place
    Internal mesh pocket conveniently stores power cords
    Compact case to store or transport smaller portable hard drives


  • Case Logic

    Case Logic CDE-48 48 Capacity Heavy Duty CD Wallet, Black

    CE (Case Logic)
    List Price: $12.99
    Price: $8.59
    You Save: $4.40 (34%)

    Patented polypropylene Prosleeves keep dirt away to prevent scratching of delicate CD surface
    Durable molded outer case protects 48 CDs or 24 with liner notes


  • Case Logic

    Case Logic DLC-115 15.6-Inch Laptop and Tablet Briefcase (Black)

    CE (Case Logic)

    Rating (453 reviews):
    (4.5/5)
    Case Logic

    Good lightweight briefcase to hold both a 15-inch laptop and my iPad 2, but may be too slim if your AC adapter brick is thick.

    இ Fuzzy Wuzzy's Summary:ѾѾѾѾ Recommended with warm fuzzies (but the slim interior space is better suited either for a laptop with a compact slim AC adapter, or an 11-inch or 13-inch ultrabook or MacBook Air).The first thing that I noticed about this laptop briefcase was how light and slim it was. This briefcase only weighs 21 ounces (1 pound 5 ounces), including the shoulder strap, which is lighter than many laptop bags. The exterior feels like soft neoprene while all interiors are lined with nylon. The main laptop compartment has dimensions of 15.25 inches wide and 11.25 inches deep, and can accomodate a laptop of 15.2"x10.5"x1.7". Inside the main laptop compartment is an 8.0-inch wide sleeve that perfectly fits my iPad 2. My iPad 2 is covered with the excellent ... 4/5 ƒůŽźŸ ωŬ&#... - See all my reviews, January 8, 2012

    Zipper Broke

    0 2/5 tampaloser - See all my reviews Verified Purchase(What's this?) This review is from: Case Logic DLC-115 15.6-Inch Laptop and Tablet Briefcase (Black) (Personal Computers) Upon receiving the bag I was pleased by the appearance and slimness, but as I slipped my laptop in and went to zip it up the zipper would not mesh together and left the bag hanging open on either side of the zipper. As I slid it back and fourth to try and get it to catch the ZIPPER BROKE.Initially I planned to get a replacement sent but as I read reviews citing the bag's slim profile impeding storage I experimented with it and found that the slim bag bulges awkwardly when storing blocky objects like AC adapters and mice, in the end I got a refundSummary of my experience-broken zipper-no space for ac adapter-chose refund 0 Help other customers find the most helpful reviews  Was this review helpful to you? , June 29, 2012

    Perfect step up from a laptop sleeve

    0 5/5 Patrick J. Sweeney - See all my reviews, July 17, 2012
    List Price: $44.99
    Organization panel inside the front pocket stores your cell phone, iPod and business essentials while also allowing plenty of space for power cords
    Dedicated laptop compartment sized to fit laptops with up to a 15.6 inch display
    Zippered back panel pocket with integrated smartphone slip pocket provides discrete storage for items you want to keep close at your side
    Elevated, nylex-lined, padded pocket protects up to a 10.1 inch tablet
    Pass through along the back panel easily slips over the handle of rolling luggage
    Neoprene-padded carry handles and a removable no-slip shoulder strap provide comfortable carrying options


  • Case Logic

    Case Logic AUA-311 11.6-Inch Laptop and iPad Slim Case (Black)

    Personal Computer (Case Logic)

    Rating (352 reviews):
    (4.7/5)
    Case Logic

    Excellent bag for minimalist travel - just check your laptop dimensions first

    0 5/5 Lon J. Seidman "lon@ lon.tv" (CT) - See all my reviews, November 3, 2012

    The Biking Jersey of eDevice Cases

    I have purchased several CaseLogic items over the years. In every instance, after a few years, I needed something different long before it showed appreciable signs of wear - the mark of a properly made product.If minimizing the footprint of your current set of must-have electronic devices (smartphone, iPad, laptop and associated cords and power adapters) is the goal, this is the product of choice. There is not room for much else, though, so when you add the included shoulder strap (with its wide rubber pad) to the contents of the case, and perhaps a slim external drive, it will begin to bulge. As another reviewer noted, a pad of writing paper would feel squeezed.My iPhone 4 is in an Otterbox and is able to slide - though snugly - into the middle of the three sub-pockets of the external section. If both a laptop and iPad were present in their designated slots of the main section, you'd probably want the iPhone in the external-most zippered pocket, where the... 4/5 Canthespam (San Francisco, CA) - See all my reviews, December 20, 2012

    Attractive, slim and a good value

    For some reason, it's been very hard to find a moderately priced, slim, and reasonably attractive case for a 14 inch laptop. The Case Logic AUA-314 in black fits those requirements nicely.The case is very slim and compact. The interior pockets are very basic, but all I really need. This won't carry much besides the computer, but most of the time that's fine.My biggest objection is the strap, it seems cheap looking though I imagine it's fine in terms of strength. It's not as nice as the strap on the other Case Logic cases I've owned. (Compare the strap for the VNA214, below, to see what I mean. The handle on the older model is better, too.)While this case isn't meant to stop bullets, I wish there was a little more padding and reinforcement, for those times when you accidentally bump the computer.I'm not a fan of the vertical zipper on the front pocket for the phone, it makes the pocket of limited use for anything else. Most people... 4/5 Snap, Crackle and Pop (United States) - See all my reviews This review is from: Case Logic AUA-314 14.1-Inch Laptop/ MacBook Air / Pro Retina Display and iPad Slim Case (Black) (Personal Computers) For some reason, it's been very hard to find a moderately priced, slim, and reasonably attractive case for a 14 inch laptop. The Case Logic AUA-314 in black fits those requirements nicely.The case is very slim and compact. The interior pockets are very basic, but all I really need. This won't carry much besides the computer, but most of the time that's fine.My biggest objection is the strap, it seems cheap looking though I imagine it's fine in terms of strength. It's not as nice as the strap on the other Case Logic cases I've owned. (Compare the strap for the VNA214, below, to see what I mean. The handle on the older model is better, too.)While this case isn't meant to stop bullets, I wish there was a little more padding and reinforcement, for those times when you accidentally bump the computer.I'm not a fan of the vertical zipper on the front pocket for the phone, it makes the pocket of limited use for anything else. Most people... Read more Help other customers find the most helpful reviews  Was this review helpful to you? , February 12, 2013
    List Price: $34.99
    Luggage strap securely attaches slim case to most rolling luggage
    Fits Devices (l x w x h): 11.8 x 0.9 x 8.3 in
    Organizer panel in front pocket with dedicated storage for external hard drive, pens and other accessories
    Zippered front pocket keeps your smartphone secure yet easily accessible
    Comfortable, removable shoulder strap and padded handle for easy portability
    Front pocket stores bulky power cords neatly in the bottom and out of the way


  • CASE LOGIC

    Case Logic SLRC-206 SLR Camera and 15.4-Inch Laptop Backpack (Black)

    Photography (CASE LOGIC)

    Rating (794 reviews):
    (4.6/5)
    CASE LOGIC

    Great backpack but with a couple of minor drawbacks

    This is a great camera backpack, and for the price, can't really be beat. However, there are a couple of things that I dislike about the bag.1) The padded dividers are quite thick and take up a chunk of space within the backpack.2) The hammock system for the camera is neat but it also results in a lot of wasted space at the top of the backpack on either side of where the DSLR body sits.3) The zipper for the main flap goes down all the way to the bottom but due to the rubberized "bucket" at the bottom, has to stop above the bucket section at the base of the backpack. This is inconvenient because the lower most compartments of the backpack are hard to get at since the flap cannot be pulled apart any more. That space is pretty much dead space because anything that is stored in there will not be easily accessible unless you lay the bag completely flat and then struggle a bit with pulling your lens out of the bottom most compartment.4) The... 4/5 Orion "SM" (USA) - See all my reviews Verified Purchase(What's this?) This review is from: Case Logic SLRC-206 SLR Camera and 15.4-Inch Laptop Backpack (Black) (Camera) This is a great camera backpack, and for the price, can't really be beat. However, there are a couple of things that I dislike about the bag.1) The padded dividers are quite thick and take up a chunk of space within the backpack.2) The hammock system for the camera is neat but it also results in a lot of wasted space at the top of the backpack on either side of where the DSLR body sits.3) The zipper for the main flap goes down all the way to the bottom but due to the rubberized "bucket" at the bottom, has to stop above the bucket section at the base of the backpack. This is inconvenient because the lower most compartments of the backpack are hard to get at since the flap cannot be pulled apart any more. That space is pretty much dead space because anything that is stored in there will not be easily accessible unless you lay the bag completely flat and then struggle a bit with pulling your lens out of the bottom most compartment.4) The... Read more Help other customers find the most helpful reviews  Was this review helpful to you? , December 15, 2010

    ********** 10 STARS ON THIS SLRC-206 CASE!!!! GREAT BUY!!!

    WOW, is where I will start, this case gets 10 STARS! In the past I reviewed the Case Logic XN SLR-6 med. case and it had MANY flaws. ALL of those flaws have been corrected on this new SLRC-206 case. The area where the camera body goes is now UNIVERSAL! ANY body will now fit this case even with a Canon 300mm L lens attached, hood reversed! My 20D even fits perfect with a battery grip attached, It is totally universal, BEAUTIFUL! There is now padding all around even the flap that goes around the top over the camera body! The padding is very substantial all over this case, even the small pieces that hold your lenses in place are very thickly padded, moveable and and contoured to hold everything secure. Everything inside is moveable with velcro, even the rubber sling piece the lens slips through, completely adjustable for any use, you can even take out everything inside and use it as a regular backpack! I LOVE THIS CASE and I thank case logic for listening to my review and correcting... 5/5 P. Cannon (Big Pine Key, Florida United States) - See all my reviews, October 20, 2009

    Another fantastic product from CaseLogic

    This is a very well thought out bag that really stands out from others in its class. For someone like me, who travels with their gear and does a good bit of hiking and camping, a rugged bag is essential.The organizational possibilities are endless with this pack. The interior is composed of numerous foam components (coated in soft felt) equipped with Velcro. It is super easy to rearrange the padding inside to give any lens a snug fit. I threw in my 200mm zoom and 1.4 prime lenses today, quickly readjusted the padding, zipped it up, and I was out the door without a worry. Of course, I still had room for about four other lenses. I also had my 20-year-old Minolta camera in there, and the design of the hammock and the way the padding angled around the camera body gave it a very secure fit. The memory foam designed to sit on top of the camera body is dense, but it is covered in felt and seems safe enough to have pressed against the display screen of a DSLR. In short,... 5/5 Senor Zoidbergo (Washington D.C.) - See all my reviews, December 20, 2009
    List Price: $119.99
    Water-proof EVA base withstands the elements and allows the backpack to stand up on its own
    Memory foam on interior of backpack lid helps protect your delicate LCD screen
    Backpack holds SLR camera body with attached zoom lens, laptop and additional accessories
    Memory foam on interior of backpack lid helps protect your delicate LCD screen
    Backpack holds SLR camera body with attached zoom lens, laptop and additional accessories
    Patent pending hammock system suspends your SLR above the bottom of case, providing superior impact protection
    Fits Laptops dimensions: 15.4-Inch x 10.4-Inch x 1-Inch
    Fits Laptops dimensions: 15.4-Inch x 10.4-Inch x 1-Inch
    Patent pending hammock system suspends your SLR above the bottom of case, providing superior impact protection
    Water-proof EVA base withstands the elements and allows the backpack to stand up on its own


  • Case Logic

    Case Logic CD/DVDW-208 224 Capacity Classic CD/DVD Wallet (Black)

    CE (Case Logic)
    List Price: $44.99
    Price: $23.15
    You Save: $21.84 (49%)

    Durable and padded nylon exterior protects your CDs
    Durable padded outer-material resistant to heat, moisture, and tearing
    Patented protective ProSleeves keep dirt away to prevent scratching of delicate CD surface
    Holds 208 CDs or 104 with liner notes
    Fast File holds an additional 16 CDs, use it to keep your favorite CDs easy to access


Camera and Photo Accessories


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Pretzel Logic iPhone 4 Savvy Case iPhone 4/4S Cover

purple, fuchsia, green, geometric, pink, pattern,
Savvy iPhone 4 hardshell case design from "Pretzel Logic," an Apophysis fractal by Susan Wallace. Copyright © 2008, Susan Wallace. An array of tri-lobed shapes in shades of purple, fuchsia and green repeat endlessly in this lively abstract design.
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Pretzel Logic iPad Air Case

purple, fuchsia, green, geometric, pink, pattern,
iPad Air case design from "Pretzel Logic," an Apophysis fractal by Susan Wallace. Copyright © 2008, Susan Wallace. An array of tri-lobed shapes in shades of purple, fuchsia and green repeat endlessly in this lively abstract design.
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