Bruno Woltzenlogel Paleo - Academia.edu (original) (raw)

Events by Bruno Woltzenlogel Paleo

This was the 4th world congress organized about the square of opposition after very succesful pre... more This was the 4th world congress organized about the square of opposition after very succesful previous editions in Montreux, Switzerland 2007, Corté, Corsica 2010, Beirut, Lebanon, 2012. An interdisciplinary event gathering logicians, philosophers, mathematicians, semioticians, theologians, cognitivists, artists and computer scientists.
http://www.square-of-opposition.org/square2014.html

Papers by Bruno Woltzenlogel Paleo

In database record linkage or natural language processing tasks one usually encounters problems w... more In database record linkage or natural language processing tasks one usually encounters problems when working with data or texts containing noise, typos and other kinds of errors. In this thesis the use of modified Levenshtein edit distances to deal with these problems is investigated. For the task of linking distinct records representing the same entity in a database we used and extended the WEKA API for Machine Learning, obtaining good precision and recall results. For the task of searching and annotating occurrences of specified words in texts written in natural language we implemented an approximate Gazetteer for GATE, the General Architecture for Text Engineering.

Lecture Notes in Computer Science, 2015

logic.at, 2010

A sequent Γ⊣∆ is a pair of multisets (the antecedent Γ and the succedent∆) of formulas in the lan... more A sequent Γ⊣∆ is a pair of multisets (the antecedent Γ and the succedent∆) of formulas in the language of predicate logic. A sequent calculus proof is a tree of inferences, composed of a conclusion sequent (below the inference line) and zero or more premises (above the inference line). Some examples of inference rules are:

Journal of Automated Reasoning

Mathematical Structures in Computer Science

Resolution and sequent calculus are two well-known formal proof systems. Their differences make t... more Resolution and sequent calculus are two well-known formal proof systems. Their differences make them suitable for distinct tasks. Resolution and its variants are very efficient for automated reasoning and are in fact the theoretical basis of many theorem provers. However, being intentionally machine oriented, the resolution calculus is not as natural for human beings and the input problem needs to be pre-processed to clause normal form. Sequent calculus, on the other hand, is a modular formalism that is useful for analysing meta-properties of various logics and is, therefore, popular among proof theorists. The input problem does not need to be pre-processed, and proofs are more detailed. However, proofs also tend to be larger and more verbose. When the worlds of proof theory and automated theorem proving meet, translations between resolution and sequent calculus are often necessary. In this paper, we compare three translation methods and analyse their complexity.

Mathematical Structures in Computer Science

Classical and Quantum Gravity, 2004

We are building the Schenberg gravitational wave detector at the Physics Institute of the Univers... more We are building the Schenberg gravitational wave detector at the Physics Institute of the University of São Paulo as programmed by the Brazilian Graviton Project. The antenna and its vibration isolation system are already built, and we have made a first cryogenic run for an overall test, in which we measured the antenna mechanical Q (figure of merit). We also have built a 10.21 GHz oscillator with phase noise performance better than −120 dBc at 3.2 kHz to pump an initial CuAl6% two-mode transducer. We plan to prepare this spherical antenna for a first operational run at 4.2 K with a single transducer and an initial target sensitivity of h ∼ 2 × 10 −21 Hz −1/2 in a 50 Hz bandwidth around 3.2 kHz soon. Here we present details of this plan and some recent results of the development of this project.

The axioms in Gödel's ontological proof (Scott, 2004) entail what is called modal collapse (Sobel... more The axioms in Gödel's ontological proof (Scott, 2004) entail what is called modal collapse (Sobel, 1987, 2004): the formula í µí¼ → □í µí¼ holds for any formula í µí¼ and not just for ∃í µí±¥. í µí°ºí µí±í µí±(í µí±¥) as intended. This fact has led to strong criticism of the argument and stimulated attempts to remedy the problem. One of those attempts (Anderson, 1990) sparked a controversy between Hájek and Anderson regarding the redundancy of some axioms in Anderson's theory. Although Hájek (1996, 2001) rightfully claimed the redundancy of two axioms in Anderson's (1990) theory, he still seems to have accepted Anderson's rebuttal (Anderson & Gettings, 1996) and proposed three new emendations (Hájek, 2002) which contain the axioms in question. Surprisingly, our analysis shows that the two axioms are still independent in one of the emendations, and superfluous in all of them. The controversy over the superfluousness of the two axioms indicates a trend to reduce the ontological argument to its bare essentials. In this regard, Anderson (1990) introduces another variant of the argument in which many of the axioms become derivable. A high level of minimality is also achieved by Bjørdal (1998) by taking the property of being God-like as a primitive. Many of the properties of those variants depend on the exact modal system being used and whether constant or varying domain semantics are employed. In our work, we took these conditions into account in order to provide a thorough computer assisted analysis of the mentioned arguments.

This paper describes an embedding of higher-order modal logics in the Coq proof assistant. Coq's ... more This paper describes an embedding of higher-order modal logics in the Coq proof assistant. Coq's capabilities are used to implement modal logics in a minimalistic manner, which is nevertheless sufficient for the formalization of significant, non-trivial modal logic proofs. The elegance, flexibility and convenience of this approach, from a user perspective , are illustrated here with the successful formalization of Gödel's ontological argument.

The contextual natural deduction calculus (ND c) extends the usual natural deduction calculus (ND... more The contextual natural deduction calculus (ND c) extends the usual natural deduction calculus (ND) by allowing the implication introduction and elimination rules to operate on formulas that occur inside contexts. It has been shown that, asymptotically in the best case, ND c-proofs can be quadratically smaller than the smallest ND-proofs of the same theorems. In this paper we describe the first implementation of a theorem prover for minimal logic based on ND c. Furthermore, we empirically compare it to an equally simple ND theorem prover on thousands of randomly generated conjectures.

"Computer scientists prove the existence of God " - variants of this headline appeared in the int... more "Computer scientists prove the existence of God " - variants of this headline appeared in the international press in autumn 2013. Unfortunately, many media reports had only moderate success in communicating to the wider public what had actually been achieved and what not. This article outlines the main findings of the authors' joint work in computational metaphysics. More precisely, the article focuses on their computer-supported analysis of variants and recent emendations of Kurt Gödel's modern ontological argument for the existence of God. In the conducted experiments, automated theorem provers discovered some interesting and relevant facts.

The recently developed LowerUnits algorithm compresses propositional resolution proofs generated ... more The recently developed LowerUnits algorithm compresses propositional resolution proofs generated by SAT-and SMT-solvers by postponing and lowering resolution inferences involving unit clauses, which have exactly one literal. This paper describes a generalization of this algorithm to the case of first-order resolution proofs generated by automated theorem provers. An empirical evaluation of a simplified version of this algorithm on hundreds of proofs shows promising results.

In this talk I present the new (first-order) conflict resolution calculus: an extension of the re... more In this talk I present the new (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference rule is restricted to (first-order) unit propagation and the calculus is extended with a mechanism for assuming decision literals and with a new inference rule for clause learning, which is a first-order generalization of the propositional conflict-driven clause learning (CDCL) procedure. The calculus is sound (because it can be simulated by natural deduction) and refutationally complete (because it can simulate resolution).

This was the second last talk in a seminar where much had already been said about the present and... more This was the second last talk in a seminar where much had already been said about the present and future of universality of proofs. To complement that, I decided to talk briefly about the distant past, sharing interesting facts about Leibniz, which I learned during a historical research triggered by the 300th anniversary of his death. The talk was based on an analysis of selected quotations from Leibniz, which give insight into what Leibniz would have thought if he could see today's state of the art. Leibniz was a pioneer in the topics of the seminar. Three and a half centuries ago he already dreamt of a universal logical language (characteristica universalis) and a reasoning calculus. But his contribution was not only a dream. He also took concrete initial steps to fulfil it, by defining his own language for an algebra of concepts and even describing how to encode its logical sentences into arithmetical expressions that automated calculating machines of his time could handle. While Leibniz desired a universal logical language because he had none, today we seek universality because we have too many logics and proof languages competing for acceptance. This is a clear sign of the astonishing success achieved by our community so far. Although somewhat ironic, the plurality of alternatives is a good problem to have. The potential of a universal logic for solving concrete controversies in all fields of inquiry capable of certainty was a major motivation for Leibniz. When he compares mathematics and metaphysics, Leibniz shows that he considered mathematics neither controversial enough nor in particular need of extremely precise formal reasoning. In contrast, today's applications of automated reasoning are still heavily biased towards mathematics. Despite a few exceptions, the mainstream attitude is currently not yet as universal in relation to application domains as it could be. Leibniz was also overly optimistic about how easy it would be to learn a universal logical language. He wanted it to be so simple that anyone could master it in a week or two. But the most sophisticated expressive universal languages that we have today may still require semester-long advanced courses for gifted students who already have a strong background in logic. Nevertheless, user interfaces for theorem provers have been progressing rapidly and maybe it will not take long for our technology to become universally accessible to all after only a short period of training.

Skolemization is unsound in intuitionistic logic in the sense that a Skolemiza-tion sk(F) of a fo... more Skolemization is unsound in intuitionistic logic in the sense that a Skolemiza-tion sk(F) of a formula F may be derivable in the intuitionistic sequent calculus LJ while F itself is not. This paper defines a transformation T ε that differs from Skolemization only by its use of ε-terms instead of Skolem terms; and shows that, for a simple locally restricted sequent calculus LJ , this transformation is sound: if T ε (F) is derivable in LJ , then so is F .

This paper discusses the discovery of the inconsistency in Gödel's ontological argument as a succ... more This paper discusses the discovery of the inconsistency in Gödel's ontological argument as a success story for artificial intelligence. Despite the popularity of the argument since the appearance of Gödel's manuscript in the early 1970's, the inconsistency of the axioms used in the argument remained unnoticed until 2013, when it was detected automatically by the higher-order theorem prover Leo-II. Understanding and verifying the refutation generated by the prover turned out to be a time-consuming task. Its completion, as reported here, required the reconstruction of the refutation in the Isabelle proof assistant, and it also led to a novel and more efficient way of automating higher-order modal logic S5 with a universal accessibility relation. Furthermore, the development of an improved syntactical hiding for the utilized logic embedding technique allows the refutation to be presented in a human-friendly way, suitable for non-experts in the technicalities of higher-order theorem proving. This brings us a step closer to wider adoption of logic-based artificial intelligence tools by philosophers .

Lecture Notes in Computer Science, 2015

logic.at, 2010

Journal of Automated Reasoning

Mathematical Structures in Computer Science

Classical and Quantum Gravity, 2004

This paper discusses the inconsistency in Gödel's ontological argument. Despite the popularity of... more This paper discusses the inconsistency in Gödel's ontological argument. Despite the popularity of Gödel's argument, this inconsistency remained unnoticed until 2013, when it was detected automatically by the higher-order theorem prover Leo-II. Complementing the meta-logic explanation for the inconsistency available in our IJCAI 2016 paper [6], we present here a new purely object-logic explanation that does not rely on semantic argumentation.