Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice op... more Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice operators to the generalised case of arbitrary nonmonotone operators. Approximation theory captures intuitions and principles found in several nonmonotonic reasoning systems and describes all main 2-, 3- and 4-valued semantics of logic programming, default logic and autoepistemic logic.
This paper is an analysis of two knowledge representation extensions of logic programming, namely... more This paper is an analysis of two knowledge representation extensions of logic programming, namely Answer Set Programming and ID-Logic. Our aim is to compare both logics on the level of declarative reading, practical methodology and formal semantics. At the level of methodology, we put forward the thesis that in many (but not all) existing applications of ASP, an ASP program is used to encode definitions and assertions, similar as in ID-Logic. We illustrate this thesis with an example and present a formal result that supports it, namely an equivalence preserving translation from a class of ID-Logic theories into ASP. This translation can be exploited also to use the current efficient ASP solvers to reason on ID-Logic theories and it has been used to implement a model generator for ID-Logic.
It is well known that, under certain conditions, it is possible to split logic programs under sta... more It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, that is, to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other nonmonotonic formalisms, such as auto-epistemic
In ], we defined a class of stratified auto-epistemic theories and made the claim that the models... more In ], we defined a class of stratified auto-epistemic theories and made the claim that the models of such theories under a number of different semantics (namely, (partial) expansions, (partial) extensions, Kripke-Kleene model and well-founded model) can be constructed in an incremental way, following the stratification of the theory. However, it turns out that this result only holds as long as the constructed models are consistent. This can be demonstrated by the following example.
Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice op... more Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice operators to the generalised case of arbitrary nonmonotone operators. Approximation theory captures intuitions and principles found in several nonmonotonic reasoning systems and describes all main 2-, 3- and 4-valued semantics of logic programming, default logic and autoepistemic logic.
This paper is an analysis of two knowledge representation extensions of logic programming, namely... more This paper is an analysis of two knowledge representation extensions of logic programming, namely Answer Set Programming and ID-Logic. Our aim is to compare both logics on the level of declarative reading, practical methodology and formal semantics. At the level of methodology, we put forward the thesis that in many (but not all) existing applications of ASP, an ASP program is used to encode definitions and assertions, similar as in ID-Logic. We illustrate this thesis with an example and present a formal result that supports it, namely an equivalence preserving translation from a class of ID-Logic theories into ASP. This translation can be exploited also to use the current efficient ASP solvers to reason on ID-Logic theories and it has been used to implement a model generator for ID-Logic.
It is well known that, under certain conditions, it is possible to split logic programs under sta... more It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, that is, to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other nonmonotonic formalisms, such as auto-epistemic
In ], we defined a class of stratified auto-epistemic theories and made the claim that the models... more In ], we defined a class of stratified auto-epistemic theories and made the claim that the models of such theories under a number of different semantics (namely, (partial) expansions, (partial) extensions, Kripke-Kleene model and well-founded model) can be constructed in an incremental way, following the stratification of the theory. However, it turns out that this result only holds as long as the constructed models are consistent. This can be demonstrated by the following example.
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Papers by David Gilis