Results

**11 - 13**of**13**### Explicit Substitution into Action -- A Non-Monotone Logic for . . .

, 2002

"... A logic LP # for reasoning about change is presented. The logic, an extension of the logic of predicates with equalitu, is based on the idea that explicit substitutions can be seen as atomic formulae describing basic change of the state of a system. The logic is substructural: non-monotone and ..."

Abstract
- Add to MetaCart

A logic LP # for reasoning about change is presented. The logic, an extension of the logic of predicates with equalitu, is based on the idea that explicit substitutions can be seen as atomic formulae describing basic change of the state of a system. The logic is substructural: non-monotone and non-commutative. Its Platonic, i.e., predicate part is governed by the additive connectives, while the identity substitution and the composition of substitutions are multiplicative truth and conjunction, respectively. Potential applications of the logic are also discussed in connection to the "Frame Problem". In particular, a logical framework is presented in which the judgments relate actions with their effects---the latter described by formulae of LP # .

### A Non-monotone Logic for Reasoning about Action

"... A logic for reasoning about action is presented. The logic is based on the idea that explicit substitutions can be seen as atomic formul describing basic change of state of a system. The logic is non-monotone, i.e., it does not admit weakening in its presentation as a fragment of non-commutative lin ..."

Abstract
- Add to MetaCart

A logic for reasoning about action is presented. The logic is based on the idea that explicit substitutions can be seen as atomic formul describing basic change of state of a system. The logic is non-monotone, i.e., it does not admit weakening in its presentation as a fragment of non-commutative linear logic. Potential applications of the logic are also discussed in connection to the "Frame Problem".

### External Examiner

, 2006

"... The results reported in Part III consist of joint work with Martín Escardó [14]. All the other results reported in this thesis are due to the author, except for background results, which are clearly stated as such. Some of the results in Part IV have already appeared as [28]. Note This version of th ..."

Abstract
- Add to MetaCart

The results reported in Part III consist of joint work with Martín Escardó [14]. All the other results reported in this thesis are due to the author, except for background results, which are clearly stated as such. Some of the results in Part IV have already appeared as [28]. Note This version of the thesis, produced on October 31, 2006, is the result of completing all the minor modifications as suggested by both the examiners in the viva report (Ref: CLM/AC/497773). We develop an operational domain theory to reason about programs in sequential functional languages. The central idea is to export domaintheoretic techniques of the Scott denotational semantics directly to the study of contextual pre-order and equivalence. We investigate to what extent this can be done for two deterministic functional programming languages: PCF (Programming-language for Computable Functionals) and FPC (Fixed Point Calculus).