Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p (2013) (review revised 2019)

I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how language works. I discuss Wittgenstein's views on incompleteness, paraconsistency and undecidability and the work of Wolpert on the limits to computation. To sum it up: The Universe According to Brooklyn---Good Science, Not So Good Philosophy. Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

Adaptive logics: a parametric approach

Adaptive logics (ALs) in standard format are defined in terms of a monotonic core logic L, a distinct set of 'abnormal' formulas Omega and a strategy, which can be either reliability or minimal abnormality. In this article we we ask under which conditions the consequence relation of two ALs that use the same strategy are identical, and when one is a proper subrelation of the other. This results in a number of sufficient (and sometimes necessary) conditions on L and Omega which apply to all ALs in standard format. In addition, we translate our results to the closely related family of default assumption consequence relations

Analysis of the overall resource consumption of a Flemish dairy farm using Exergetic Life Cycle Assessment

To deal with environmental challenges such as pollution and resource depletion, the potential environmental impact of agricultural products is commonly evaluated using the Life Cycle Assessment (LCA) methodology. For livestock systems, emission-related impacts such as global warming have been frequently studied in this way. During the past decades, intensifi-cation of agricultural systems to improve yields coincided with an increased material and energy throughput. Therefore, we focus on resource consumption in this paper. We applied an exergy-based approach to quantify total resource use and to calculate resource efficien-cies, both at system level and at life cycle level. We have performed a case study of an in-tensive confinement-based dairy farm in Flanders to illustrate our approach

Minimising disjunctive information

In [5, 6], Belnap proposed a number of amendments to Rescher’s strategy for reasoning with maximal consistent subsets. More recently in [18], Horty explicitly endorsed Belnap’s amendment to address a related problem in handling inconsistent instructions and commands. In this paper, we’ll examine Belnap’s amendment and point out that Belnap’s suggestion in the use of conjunctive containment is open to the very objection he raised. We’ll propose a way out. The strategy turns on the use of First Degree Entailment in combination with Quine’s notion of prime implicate

Efficient paraconsistent reasoning with rules and ontologies for the semantic web

Ontologies formalized by means of Description Logics (DLs) and rules in the form of Logic Programs (LPs) are two prominent formalisms in the field of Knowledge Representation and Reasoning. While DLs adhere to the OpenWorld Assumption and are suited for taxonomic reasoning, LPs implement reasoning under the Closed World Assumption, so that default knowledge can be expressed. However, for many applications it is useful to have a means that allows reasoning over an open domain and expressing rules with exceptions at the same time. Hybrid MKNF knowledge bases make such a means available by formalizing DLs and LPs in a common logic, the Logic of Minimal Knowledge and Negation as Failure (MKNF). Since rules and ontologies are used in open environments such as the Semantic Web, inconsistencies cannot always be avoided. This poses a problem due to the Principle of Explosion, which holds in classical logics. Paraconsistent Logics offer a solution to this issue by assigning meaningful models even to contradictory sets of formulas. Consequently, paraconsistent semantics for DLs and LPs have been investigated intensively. Our goal is to apply the paraconsistent approach to the combination of DLs and LPs in hybrid MKNF knowledge bases. In this thesis, a new six-valued semantics for hybrid MKNF knowledge bases is introduced, extending the three-valued approach by Knorr et al., which is based on the wellfounded semantics for logic programs. Additionally, a procedural way of computing paraconsistent well-founded models for hybrid MKNF knowledge bases by means of an alternating fixpoint construction is presented and it is proven that the algorithm is sound and complete w.r.t. the model-theoretic characterization of the semantics. Moreover, it is shown that the new semantics is faithful w.r.t. well-studied paraconsistent semantics for DLs and LPs, respectively, and maintains the efficiency of the approach it extends

Externally Supported Models for Efficient Computation of Paracoherent Answer Sets

Answer Set Programming (ASP) is a well established formalism for nonmonotonic reasoning. While incoherence, the non-existence of answer sets for some programs, is an important feature of ASP, it has frequently been criticised and indeed has some disadvantages, especially for query answering. Paracoherent semantics have been suggested as a remedy, which extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. In this paper we present an alternative characterization of the two major paracoherent semantics in terms of (extended) externally supported models. This definition uses a transformation of ASP programs that is more parsimonious than the classic epistemic transformation used in recent implementations. A performance comparison carried out on benchmarks from ASP competitions shows that the usage of the new transformation brings about performance improvements that are independent of the underlying algorithms

Revision based total semantics for extended normal logic programs

Dissertação para obtenção do Grau de Doutor em Matemática - Lógica e Fundamentos da MatemáticaFundação para a Ciência e Tecnologia - SFRH/ PROTEC/49747/200

Belnap's epistemic states and negation-as-failure

Generalizing Belnap's system of epistemic states [Bel77] we obtain the system of disjunctive factbases which is the paradigm for all other kinds of disjunctive knowledge bases. Disjunctive factbases capture the nonmonotonic reasoning based on paraminimal models. In the schema of a disjunctive factbase, certain predicates of the resp. domain are declared to be exact, i.e. two-valued, and in turn some of these exact predicates are declared to be subject to the Closed-World Assumption (CWA). Thus, we distinguish between three kinds of predicates: inexact predicates, exact predicates subject to the CWA, and exact predicates not subject to the CWA

Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases

This article is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different para-MKNF knowledge bases