**mfingerime.usp.br**

Quantitative Logic Reasoning

We present a research program which investigates the intersection of deductive rea- soning with explicit quantitative capabilities. These quantitative capabilities encom- pass probabilistic reasoning, counting and counting quantifiers, and similar systems.

The need to have a combined reasoning system that enables a unified way to reason with quantities has always been recognized in modern logic, as proposals of logic prob- abilistic reasoning are present in the work of Boole [1854]. Equally ubiquitous is the need to deal with cardinality restrictions on finite sets.

We show that there is a common way to deal with these several deductive quantitative capabilities, involving a framework based on Linear Algebras and Linear Programming, and the distinction between probabilistic and cardinality reasoning arising from the different family of algebras employed.

The quantitative logic systems are particularly amenable to the introduction of in- consistency measurements, which quantify the degree of inconsistency of a given quan- titative logic theory, following some basic principles of inconsistency measurements.

Marcelo Finger is Professor of Computer Science at the Institute of Mathematics and Statistics, University of São Paulo, CNPq research grant receiver level 1B, editor of The Scientific World Journal and the Sao Paulo Journal of Mathematical Sciences, published special issues in journals such as the Annals of Mathematics in Artificial Intelligence (2001) and Theoretical Computer Science (2014).

Received his BSc in Electronic Engineering from the University of São Paulo (1988), MSc (1990) and PhD (1994) in Computing by the Imperial College, University of London (1990). He was a visiting professor in Computer Science departments in Universitée Paul Sabatier - Toulouse (2011) and Cornell University (2012-2013).

His research topics include the following: Logic, Artificial Intelligence, Databases, Digital Humanities and Computational Linguistics. He is a fellow researcher of CNPq since 1996. He has received several awards: Sesquicentennial Convocation Award (1990), Armstrong Prize and Medal (1994), Jabuti Prize (2007 -1o place, category Science, Technology and Informatics) and several awards for teaching performance (2002, 2004, 2005, 2006).

He currently conducts research involving logic, quantitative and probabilistic reasoning in order to understand the interaction between these basic ways of reasoning, their computational complexity and their applications in Artificial Intelligence, Databases, Computational Linguistics and Digital Humanities.