Andras Kornai

In 1.1 we set the stage by introducing the interpretation relation that connects linguistic expressions (words, sentences, larger texts) to their meanings, and draw a distinction between the two main parts of semantics, lexical and compositional. The enormous range of ideas, feelings, thoughts, and facts that natural language can convey makes the task of analyzing the meaning of natural language expressions very broad, and we need to prioritize. This is done in 1.2 and 1.3 based on frequency of occurrence and information content respectively. After these basics are in place, we discuss the overall plan of the book in 1.4, and the reader can then make a more informed choice about the reading plans offered in 1.5.

Learning something is not a trivial act – the ancient Greeks were quite aware of the difficulties attendant to the creation of something from nothing. If knowledge in the learner’s head can be created from nothing, the floodgates are open, and all kinds of things can be created from nothing, contrary to everyday experience. Prolepsis, often translated as ‘foreshadowing’ or ‘preconception’, is a technical term originating with the Stoics, for whom it meant a naturally endowed and innate system of thought involving universal concepts.

After a brief introduction to algebras, in 2.1 we begin with linear spaces (LSs) and Boolean algebras (BAs). In 2.2 we cover the basic notions of universal algebra, building up to, but not including, Birkhoff’s Theorem. Ultrafilters are introduced in 2.3. In 2.4 we turn to the propositional calculus, and the (lower) predicate calculus is discussed in 2.5. The elements of proof theory are sketched in 2.6, and some preliminaries from multivariate statistics (which are, for the most part, just linear algebra in new terminological garb) are discussed in 2.7. The material is selected for its utility in later chapters, rather than for internal cohesion, and is largely orthogonal to the standard logic prerequisites to compositional semantics covered in for example the two volumes of Gamut (1991). A first course in linear algebra (but not in multivariate statistics) is assumed.

Embodied cognition is the thesis that cognition is “deeply dependent upon features of the physical body of an agent, that [... ] aspects of the agent’s body beyond the brain play a significant causal or physically constitutive role in cognitive processing” (SEP). As we have only a cursory understanding of the cognitive systems of dolphins and whales, the real test of this thesis will have to wait until we can investigate space aliens or, perhaps more realistically, artificial general intelligences (AGIs).

Using an asymptotic characterization of probabilistic finite state languages over a one-letter alphabet we construct a probabilistic language with regular support that cannot be generated by probabilistic CFGs. Since all probability values used in the example are rational, our work is immune to the criticism leveled by Suppes (Synthese 22:95–116, 1970 ) against the work of Ellis ( 1969 ) who first constructed probabilistic FSLs that admit no probabilistic FSGs. Some implications for probabilistic language modeling by HMMs are discussed

The focus of this textbook is the meaning of linguistic expressions, typically full sentences and longer texts. The author describes the conceptual and formal tools required for building semantic systems capable of understanding text, both for specific tasks such as information extraction and question answering and for broad undertakings such as the Semantic Web. The goal here is to present the fundamental ideas that working systems rest on, and this book is aimed primarily at Computer Science or Engineering students interested in developing semantic systems. The ideal reader is a hacker, a person who delights in having an intimate understanding of the internal workings of a system.