Math: Logic and Foundations: Software

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ACL2 Version 2.7 http://www.cs.utexas.edu/users/moore/acl2/ A programming language in which you can model computer systems and a tool to help prove properties of those models. Available under GPL and runs on various platforms. Includes related download links. Automated Reasoning Project http://cslab.anu.edu.au/ar/ Web resource provided by research group. Includes access to software developed by the team, coverering such projects as FINDER (Finite Domain Enumerator), MaGIC (Matrix Generator for Implication Connectives) and Kripke (A theorem prover for the relevant logic LR). Bertrand http://www.humnet.ucla.edu/humnet/phil/grads/herzberg/Bertrand.html First-order satisfiability checker and prover for the Macintosh. Church http://www.alcyone.com/software/church/ Program understands the different types of lambda expressions, can extract lists of variables (both free and bound) and subterms, and can simplify complicated expressions. Uses Python. Database of Existing Mechanized Reasoning Systems http://www-formal.stanford.edu/clt/ARS/systems.html A list (>50 entries) of automatic resolution provers (like Otter), interactive provers (like PVS) and other mechanized reasoning tools. DC Proof Online http://www.dcproof.com New proof-writing software to teach the fundamentals of logic and proof. Enables users/students to write error-free proofs by selecting rules of inference, axioms, etc. from convenient drop-down menus. Includes tutorial and exercises. DELORES http://www.dfki.uni-kl.de/~miller/delores/ A forward-chaining reasoning engine for defeasible logic, a less expressive but more efficient nonmonotonic logic. Gateway to Logic http://logik.phl.univie.ac.at/~chris/formular-uk.html A collection of web-based logic programs offering a number of logical functions: interactively or automatically build proofs, check theorems, and operate on propositional logic formulae. Isabelle http://www.cl.cam.ac.uk/Research/HVG/Isabelle/ A generic theorem proving environment developed at Cambridge University (Larry Paulson) and TU Munich (Tobias Nipkow). Includes logic, documentation and free download. llprover http://bach.scitec.kobe-u.ac.jp/llprover/ A linear logic prover that searches a cut-free proof for the given two-sided sequent of first-order linear logic. Logic Software from CSLI http://www-csli.stanford.edu/hp/Logic-software.html By Jon Barwise and John Etchemendy. LOOM http://www.isi.edu/isd/LOOM/LOOM-HOME.html A language and environment for constructing intelligent applications. It is a research project in the Artificial Intelligence research group at the University of Southern California's Information Sciences Institute. The goal of the project is to develop and field advanced tools for knowledge representation and reasoning in Artificial Intelligence. Ludwig http://www.mintlogic.com/ludwig/ Application that draws truth-tables for propositional logic formulae. Available for free download and web use. LWB http://www.lwb.unibe.ch/ Logics Workbench. MUltlog http://www.logic.at/multlog/ Takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and clause formation rules for this logic. MUltseq http://www.logic.at/multseq/ A generic sequent prover for propositional finitely-valued logics. Paradox http://www.cs.chalmers.se/~koen/paradox/ A tool that processes first-order logic problems and tries to find finite-domain models for them; written by Koen Claessen and Niklas Sörensson. Haskell and C++; free download under GPL. Proof General http://proofgeneral.inf.ed.ac.uk Comprehensive Gnu-Emacs and XEmacs interface for several theorem provers including Coq, Isabelle, Lego, and Phox. ProofPower http://www.lemma-one.com/ProofPower/index/ A suite of tools supporting specification and proof in Higher Order Logic (HOL) and in Z notation. PROTEIN http://www.uni-koblenz.de/ag-ki/Implementierungen/Protein/ A PROver with a Theory Extension INterface. Theorem prover for first-order clause logic, written in ECRC's Prolog-dialect ECLiPSe. Free download, documentation. PVS http://pvs.csl.sri.com/ The PVS Specification and Verification System. Available for Sparc machines with Solaris 2 and Intel x86 Machines with Linux compatible with Redhat 5 or later. Required is Emacs (version 19 or later), recommended LaTeX and Tcl/Tk. Download by FTP. SwitchMin Digital Circuit Minimizer http://incolor.inetnebr.com/double/softlib/switchmin.html Tool for minimizing boolean logic functions. The Coq Project http://pauillac.inria.fr/coq/ Deals with effectively machine-checked formal mathematics. In practice, this includes the study of mathematical formalisms well-suited for implementations, the implementations themselves and the use of these for various applications. Focuses on software correctness proofs. Tree Proof Generator http://www.umsu.de/logik/trees An implementation of the semantic tableaux method for classical propositional and predicate logic, written in JavaScript/DOM. VeriFun http://www.informatik.tu-darmstadt.de/pm/verifun/ A semi-automated system for the verification of statements about programs written in a functional programming language. The system is capable of following fully-automated routines for theorem proving and hypotheses formation, as well as operating interactively when these reoutines fail.
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