The Journal of Functional and Logic Programming The MIT Press
... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...
... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...
Fichte`s Legacy in Logic
... The special relationship between logic and the Wissenschaftslehre follows from the above. The former does not provide the foundation for the latter; it is, instead, the latter which provides the foundation for the former. (SW I, 68) ...
... The special relationship between logic and the Wissenschaftslehre follows from the above. The former does not provide the foundation for the latter; it is, instead, the latter which provides the foundation for the former. (SW I, 68) ...
On the Complexity of Resolution-based Proof Systems
... the length of proofs in propositional logic. One of its main questions is to determine which particular propositional formulas have short proofs in a given propositional proof system. In this thesis we present several results related to this question, all on proof systems that are extensions of the ...
... the length of proofs in propositional logic. One of its main questions is to determine which particular propositional formulas have short proofs in a given propositional proof system. In this thesis we present several results related to this question, all on proof systems that are extensions of the ...
Two-Variable Logic on Data Words
... more variables are permitted, or when a linear order on the data values is available, or when more equivalence relations are available. Following [Bouyer et al. 2003], a data word is a finite sequence of positions having each a label over some finite alphabet together with a data value from an unbou ...
... more variables are permitted, or when a linear order on the data values is available, or when more equivalence relations are available. Following [Bouyer et al. 2003], a data word is a finite sequence of positions having each a label over some finite alphabet together with a data value from an unbou ...
MoL-2013-07 - Institute for Logic, Language and Computation
... Woodin’s conditional platonism [Woo04], Friedman’s inner model hypothesis [Fri06], but also due to mathematical concerns, such as to account for the curious fact that, in some sense, these techniques that we have mentioned are essentially the only known techniques that set theorists have to prove in ...
... Woodin’s conditional platonism [Woo04], Friedman’s inner model hypothesis [Fri06], but also due to mathematical concerns, such as to account for the curious fact that, in some sense, these techniques that we have mentioned are essentially the only known techniques that set theorists have to prove in ...
CERES for Propositional Proof Schemata
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
On the Complexity of Qualitative Spatial Reasoning: A Maximal
... do not have to be internally connected, i.e . a single region may consist of different disconnected parts . The domain of spatial variables (denoted as X, Y, Z) is the whole topological space. In this work we will focus on RCC-8, but most of our results can easily be applied to RCC-5, a subset of RC ...
... do not have to be internally connected, i.e . a single region may consist of different disconnected parts . The domain of spatial variables (denoted as X, Y, Z) is the whole topological space. In this work we will focus on RCC-8, but most of our results can easily be applied to RCC-5, a subset of RC ...
Reasoning about Complex Actions with Incomplete Knowledge: A
... of reasoning and acting on the basis of its (dis)beliefs. In particular, an agent might want to take actions to acquire new knowledge on the world, if its knowledge is incomplete. These knowledge producing actions are usually called sensing actions. In this paper, we aim at extending the action lang ...
... of reasoning and acting on the basis of its (dis)beliefs. In particular, an agent might want to take actions to acquire new knowledge on the world, if its knowledge is incomplete. These knowledge producing actions are usually called sensing actions. In this paper, we aim at extending the action lang ...
A Logical Framework for Default Reasoning
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
ATL with Strategy Contexts and Bounded Memory
... first, while ATL strategy quantifiers drop strategies introduced by earlier quantifiers in the evaluation of the formula, our logics keep executing those strategies. To achieve this idea, we naturally adapt the semantics of ATL in order to interpret a formula within a stategy context. Our new strategy ...
... first, while ATL strategy quantifiers drop strategies introduced by earlier quantifiers in the evaluation of the formula, our logics keep executing those strategies. To achieve this idea, we naturally adapt the semantics of ATL in order to interpret a formula within a stategy context. Our new strategy ...
Syllogisms
... of all that is treated in logic (both intentional and symbolic), I have decided to focus simply on the categorical syllogism. Terms: Logic: the study of how to reason well. Reasoning, recall, is the third act of the intellect. Validity: Valid thinking is thinking in conformity with the rules. If t ...
... of all that is treated in logic (both intentional and symbolic), I have decided to focus simply on the categorical syllogism. Terms: Logic: the study of how to reason well. Reasoning, recall, is the third act of the intellect. Validity: Valid thinking is thinking in conformity with the rules. If t ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and secon ...
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and secon ...
Harmony, Normality and Stability
... stability would obtain; otherwise not.’ (LBM 288) In this section, Dummett only talks of rules of inference which are determined from each other, so the criterion is one applied to the forms of rules of inference by themselves, not relative to formal systems they may be part of. Dummett, it is fair ...
... stability would obtain; otherwise not.’ (LBM 288) In this section, Dummett only talks of rules of inference which are determined from each other, so the criterion is one applied to the forms of rules of inference by themselves, not relative to formal systems they may be part of. Dummett, it is fair ...
Document
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
Document
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
Hybrid, Classical, and Presuppositional Inquisitive Semantics
... • Since the interrogative ?{p , q} is to be a question, is has to be non-informative. The disjunct marked in red takes care of that. • If we read ?{p , q} as an alternative question, it may be observed that the answers p and q do not have the same status as the answer ¬p ∧ ¬q. • Already for the pola ...
... • Since the interrogative ?{p , q} is to be a question, is has to be non-informative. The disjunct marked in red takes care of that. • If we read ?{p , q} as an alternative question, it may be observed that the answers p and q do not have the same status as the answer ¬p ∧ ¬q. • Already for the pola ...
Inferential Erotetic Logic meets Inquisitive Semantics. Research
... concepts. In order to define them one needs, inter alia, a certain concept of entailment for declaratives. However, in its general setting IEL is neutral in the controversy concerning what “The Logic” of declaratives is. One can use Classical Logic, but non-classical logics are also permitted. In th ...
... concepts. In order to define them one needs, inter alia, a certain concept of entailment for declaratives. However, in its general setting IEL is neutral in the controversy concerning what “The Logic” of declaratives is. One can use Classical Logic, but non-classical logics are also permitted. In th ...
Gentzen`s original consistency proof and the Bar Theorem
... wanted a way to understand the truth of a sentence of number theory that is in some sense ‘finitary’ but at the same time supported classical reasoning in number theory. In this respect, the original paper as well as the 1936 paper go beyond the original Hilbert program of finding finitary consisten ...
... wanted a way to understand the truth of a sentence of number theory that is in some sense ‘finitary’ but at the same time supported classical reasoning in number theory. In this respect, the original paper as well as the 1936 paper go beyond the original Hilbert program of finding finitary consisten ...
5 model theory of modal logic
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...
logic for the mathematical
... Then there are four chapters on 1st order logic, each analogous to the one four earlier on propositional logic. One feature of the proof theory is that we deal with both common approaches to the treatment of non-sentence formulae, giving the appropriate deduction theorem and completeness (and a slig ...
... Then there are four chapters on 1st order logic, each analogous to the one four earlier on propositional logic. One feature of the proof theory is that we deal with both common approaches to the treatment of non-sentence formulae, giving the appropriate deduction theorem and completeness (and a slig ...
Frege, Boolos, and Logical Objects
... and systematized E. Mally’s [1912] distinction between two modes of predication. Mally distinguished between an object’s ‘satisfying’ a property and an object’s being determined by a property. The formal reconstruction of Mally’s distinction was used to identify ‘intentional objects’ (such as fiction ...
... and systematized E. Mally’s [1912] distinction between two modes of predication. Mally distinguished between an object’s ‘satisfying’ a property and an object’s being determined by a property. The formal reconstruction of Mally’s distinction was used to identify ‘intentional objects’ (such as fiction ...