Howard A. Blair

NeSy Conference 2016 Conference Paper

Heterotic Continuous Time Real-valued/Boolean-valued Networks

• Daniel R. Patten
• Howard A. Blair

LPAR Conference 1992 Conference Paper

General Model Theoretic Semantics for Higher-Order Horn Logic Programming

• Mino Bai
• Howard A. Blair

Abstract We introduce model-theoretic semantics [6] for Higher-Order Horn logic programming language. One advantage of logic programs over conventional non-logic programs has been that the least fixpoint is equal to the least model, therefore it is associated to logical consequence and has a meaningful declarative interpretation. In simple theory of types [9] on which Higher-Order Horn logic programming language is based, domain is dependent on interpretation [10]. To define T P operator for a logic program P, we need a fixed domain without regard to interpretation which is usually taken to be a set of atomic propositions. We build a semantics where we can fix a domain while changing interpretations. We also develop a fixpoint semantics based on our model, and show that we can get the least fixpoint which is the least model. Using this fixpoint we prove the completeness of the interpreter of our language in [14].

TCS Journal 1989 Journal Article

Paraconsistent logic programming

• Howard A. Blair
• V.S. Subrahmanian

This paper makes two contributions. First, we give a semantics for sets of clauses of the syntactic form L0 ⇍ L1 &⋯& Ln where each Li is a literal. We call such clauses generally Horn clauses. Any such endeavour has to give a coherent, formal treatment of inconsistency (in the sense of two-valued logic). Thus, as a second contribution, we give a robust semantics for generally Horn programs that allows us to “make sense” of sets of generally Horn clauses that are inconsistent (in the two-valued logic sense). This applies to the design of very large knowledge bases where inconsistent information is often present.