# Reconstructing Propositional Calculus in Database Semantics

Roland Hausser (Universität Erlangen-Nürnberg)This talk presents a reconstruction of propositional calculus as a simplified version of natural language used for communication. This requires a number of changes with respect to the traditional approach,

First, the method must be changed from the meta-language definitions of old
logic to a declarative specification for computer software. Second, the
*realist ontology* of old logic, treating meaning as a direct relation between
sentences and the *world* (defined as a set-theoretic model) must be replaced
by a functional system comprising an agent’s cognitive operations. Third, the
syntax of propositional calculus must be adapted to the time-linear nature of
language. Fourth, the truth conditional semantics of propositional calculus
must be integrated into the time-linear process of communication.

The latter task requires solutions to the following problems: First, whether an expression like p & ~p… is contradictory cannot be decided in a time- linear interpretation until the continuation, e.g., p & ~p v q…, is known; second, using truth conditions for checking consistency must avoid the SAT problem, which is known to be computationally intractable.

The reconstruction is presented as the declarative specification of a computer program, comprising (i) a data structure for storing formulas of propositional calculus as concatenated propositions, and (ii) LA-grammars for conceptualization, production, and interpretation. Written at a high level of abstraction, the reconstruction provides a comparison between the metalan\-guage-based approach of traditional logic and the procedural model of communication of database semantics.

Short vita : Professor Roland Hausser heads the Department of Computational Linguistics at the University Erlangen-Nürnberg in Germany. He has worked in formal semantics, grammar algorithms, and human-computer communication. Publications include several books, the latest foundations of Computational Linguistics, as well as papers in the AI Journal and the Journal of Theoretical Computer Science.